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------------------------------------------------------------------------ + \par 10 9 8 7 6 4 3 2 \par 630 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 2 \par ln((x - 1/2) + 3/4) \par ---------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 6 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par ln(x - 1) \par ---------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 4 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par ln(x + 1) \par ----------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 12 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 2 \par 1669 x \par ------------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 2520 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 3 \par 3853 x \par ------------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 1260 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 4 \par 61 x \par ----------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 90 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 5 \par 1577 x \par ------------------------------------------------------------------------ + \par 10 9 8 7 6 4 3 2 \par 180 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 6 \par 175 x \par ----------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 18 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 7 \par 49 x \par ----------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 18 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 8 \par 197 x \par ----------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 18 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 9 \par 109 x \par ----------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 18 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 10 \par 3 x \par ---------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 2 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 11 \par 13 x \par ---------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 4 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 12 \par 3 x \par ---------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 2 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 13 \par x \par ---------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 4 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 67 \par ------------------------------------------------------------------------ - \par 10 9 8 7 6 4 3 2 \par 280 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par / / 1/2 \\ \\ \par 1/2 | | 2 3 (x - 1/2) | | \par 3 | 2 arctan| ---------------- | - PI | \par \\ \\ 3 / / \par ----------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 54 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 2 2 \par x ln((x - 1/2) + 3/4) \par ---------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 2 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 3 2 \par 4 x ln((x - 1/2) + 3/4) \par ---------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 3 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 4 2 \par 7 x ln((x - 1/2) + 3/4) \par ---------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 3 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 6 2 \par 7 x ln((x - 1/2) + 3/4) \par ---------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 3 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 7 2 \par 4 x ln((x - 1/2) + 3/4) \par ---------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 3 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 8 2 \par x ln((x - 1/2) + 3/4) \par ---------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 2 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 9 2 \par 2 x ln((x - 1/2) + 3/4) \par ---------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 3 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 10 2 \par x ln((x - 1/2) + 3/4) \par ---------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 6 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 2 \par 3 x ln(x - 1) \par ---------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 4 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 2 \par x ln(x + 1) \par ---------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 4 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 3 \par 2 x ln(x - 1) \par ------------------------------------------------------------------ - \par 10 9 8 7 6 4 3 2 \par - x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1 \par \par 3 \par 2 x ln(x + 1) \par ---------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 3 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 4 \par 7 x ln(x - 1) \par ---------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 2 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 4 \par 7 x ln(x + 1) \par ---------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 6 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 6 \par 7 x ln(x - 1) \par ---------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 2 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 6 \par 7 x ln(x + 1) \par ---------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 6 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 7 \par 2 x ln(x - 1) \par ------------------------------------------------------------------ + \par 10 9 8 7 6 4 3 2 \par - x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1 \par \par 7 \par 2 x ln(x + 1) \par ---------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 3 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 8 \par 3 x ln(x - 1) \par ---------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 4 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 8 \par x ln(x + 1) \par ---------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 4 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 9 \par x ln(x - 1) \par ------------------------------------------------------------------ - \par 10 9 8 7 6 4 3 2 \par - x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1 \par \par 9 \par x ln(x + 1) \par ---------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 3 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 10 \par x ln(x - 1) \par ---------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 4 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 10 \par x ln(x + 1) \par ----------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 12 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par 2 \par 2 x ln((x - 1/2) + 3/4) \par ---------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 3 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par x ln(x - 1) \par ------------------------------------------------------------------ + \par 10 9 8 7 6 4 3 2 \par - x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1 \par \par x ln(x + 1) \par ---------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 3 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par / / 1/2 \\ \\ \par 1/2 | | 2 3 (x - 1/2) | | \par 2 3 x | 2 arctan| ---------------- | - PI | \par \\ \\ 3 / / \par ----------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 27 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par / / 1/2 \\ \\ \par 1/2 2 | | 2 3 (x - 1/2) | | \par 3 x | 2 arctan| ---------------- | - PI | \par \\ \\ 3 / / \par ----------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 18 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par / / 1/2 \\ \\ \par 1/2 3 | | 2 3 (x - 1/2) | | \par 4 3 x | 2 arctan| ---------------- | - PI | \par \\ \\ 3 / / \par ----------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 27 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par / / 1/2 \\ \\ \par 1/2 4 | | 2 3 (x - 1/2) | | \par 7 3 x | 2 arctan| ---------------- | - PI | \par \\ \\ 3 / / \par ----------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 27 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par / / 1/2 \\ \\ \par 1/2 6 | | 2 3 (x - 1/2) | | \par 7 3 x | 2 arctan| ---------------- | - PI | \par \\ \\ 3 / / \par ----------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 27 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par / / 1/2 \\ \\ \par 1/2 7 | | 2 3 (x - 1/2) | | \par 4 3 x | 2 arctan| ---------------- | - PI | \par \\ \\ 3 / / \par ----------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 27 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par / / 1/2 \\ \\ \par 1/2 8 | | 2 3 (x - 1/2) | | \par 3 x | 2 arctan| ---------------- | - PI | \par \\ \\ 3 / / \par ----------------------------------------------------------------------- - \par 10 9 8 7 6 4 3 2 \par 18 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par / / 1/2 \\ \\ \par 1/2 9 | | 2 3 (x - 1/2) | | \par 2 3 x | 2 arctan| ---------------- | - PI | \par \\ \\ 3 / / \par ----------------------------------------------------------------------- + \par 10 9 8 7 6 4 3 2 \par 27 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par / / 1/2 \\ \\ \par 1/2 10 | | 2 3 (x - 1/2) | | \par 3 x | 2 arctan| ---------------- | - PI | \par \\ \\ 3 / / \par ----------------------------------------------------------------------- \par 10 9 8 7 6 4 3 2 \par 54 (- x + 4 x - 3 x - 8 x + 14 x - 14 x + 8 x + 3 x - 4 x + 1) \par \par \pard\ri4\plain\f2\fs22\cf0 03. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}rule:=Rule(a*ln(`#x`),0): \par \pard\li600\ri1\fi-300\plain\f3\fs22\cf1 rat:=simplify(map(numer(integral),z->if Rule::apply(rule,z)=FAIL then z else Rule::apply(rule,z) end_if)/denom(integral)) \par \pard\li50\ri6\plain\f3\fs22\cf2\protect \par \pard\li50\ri2\plain\f3\fs22\cf2\protect / 1/2 / 1/2 / 2 x \\ \\ 1/2 2 \par | 280 3 arctan| 3 | --- - 1/3 | | - 140 3 PI - 3876 x + 5007 x - \par \\ \\ \\ 3 / / \par \par 3 4 5 6 7 8 9 \par 23118 x + 5124 x + 66234 x - 73500 x - 20580 x + 82740 x - 45780 x - \par \par 10 11 12 13 \par 11340 x + 24570 x - 11340 x + 1890 x + \par \par 1/2 2 / 1/2 / 2 x \\ \\ \par 840 3 x arctan| 3 | --- - 1/3 | | + \par \\ \\ 3 / / \par \par 1/2 3 / 1/2 / 2 x \\ \\ \par 2240 3 x arctan| 3 | --- - 1/3 | | - \par \\ \\ 3 / / \par \par 1/2 4 / 1/2 / 2 x \\ \\ \par 3920 3 x arctan| 3 | --- - 1/3 | | + \par \\ \\ 3 / / \par \par 1/2 6 / 1/2 / 2 x \\ \\ \par 3920 3 x arctan| 3 | --- - 1/3 | | - \par \\ \\ 3 / / \par \par 1/2 7 / 1/2 / 2 x \\ \\ \par 2240 3 x arctan| 3 | --- - 1/3 | | - \par \\ \\ 3 / / \par \par 1/2 8 / 1/2 / 2 x \\ \\ \par 840 3 x arctan| 3 | --- - 1/3 | | + \par \\ \\ 3 / / \par \par 1/2 9 / 1/2 / 2 x \\ \\ \par 1120 3 x arctan| 3 | --- - 1/3 | | - \par \\ \\ 3 / / \par \par 1/2 10 / 1/2 / 2 x \\ \\ 1/2 \par 280 3 x arctan| 3 | --- - 1/3 | | + 560 3 PI x - \par \\ \\ 3 / / \par \par 1/2 / 1/2 / 2 x \\ \\ 1/2 2 \par 1120 3 x arctan| 3 | --- - 1/3 | | - 420 3 PI x - \par \\ \\ 3 / / \par \par 1/2 3 1/2 4 1/2 6 1/2 7 \par 1120 3 PI x + 1960 3 PI x - 1960 3 PI x + 1120 3 PI x + \par \par 1/2 8 1/2 9 1/2 10 \\ \par 420 3 PI x - 560 3 PI x + 140 3 PI x + 1809 | / \par / \par \par 10 9 8 7 6 4 \par (7560 x - 30240 x + 22680 x + 60480 x - 105840 x + 105840 x - \par \par 3 2 \par 60480 x - 22680 x + 30240 x - 7560) \par \par \pard\ri4\plain\f2\fs22\cf0 04. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}p:=numer(r) \par \pard\li50\ri6\plain\f3\fs22\cf2\protect 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}\plain\f3\fs22\cf2\protect \par \pard\li50\ri2\plain\f3\fs22\cf2\protect \par \pard\ri4\plain\f2\fs22\cf0 12. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}s:=normal(p-q*(diff(a/b,x)+c/d)) \par \pard\li50\ri6\plain\f3\fs22\cf2\protect \par \pard\li50\ri2\plain\f3\fs22\cf2\protect 12 x + 6 x aa[0] + 3 x aa[1] + 2 x aa[2] - 16 x bb[0] + 4 x bb[1] - \par \par 2 2 3 2 3 \par 6 x aa[0] + 6 x aa[1] + 10 x aa[0] + 2 x aa[2] - 5 x aa[1] + \par \par 2 3 4 3 4 3 \par 3 x aa[3] + 6 x aa[2] + 9 x aa[1] + x aa[3] - 4 x aa[2] + 4 x aa[4] + \par \par 4 5 5 4 5 \par 6 x aa[3] + 8 x aa[2] - 3 x aa[3] + 5 x aa[5] + 6 x aa[4] + \par \par 6 5 6 5 6 7 \par 7 x aa[3] - x aa[5] - 2 x aa[4] + 6 x aa[6] + 6 x aa[5] + 6 x aa[4] - \par \par 6 7 6 7 8 7 \par 2 x aa[6] - x aa[5] + 7 x aa[7] + 6 x aa[6] + 5 x aa[5] - 3 x aa[7] + \par \par 7 8 9 8 9 8 \par 8 x aa[8] + 6 x aa[7] + 4 x aa[6] - 4 x aa[8] + x aa[7] + 9 x aa[9] + \par \par 9 10 9 10 10 \par 6 x aa[8] + 3 x aa[7] - 5 x aa[9] + 2 x aa[8] + 6 x aa[9] + \par \par 11 11 12 2 2 \par 2 x aa[8] + 3 x aa[9] + x aa[9] + 12 x bb[0] - 16 x bb[1] + \par \par 3 2 3 4 3 \par 32 x bb[0] + 4 x bb[2] + 12 x bb[1] - 56 x bb[0] - 16 x bb[2] + \par \par 4 3 4 5 6 \par 32 x bb[1] + 4 x bb[3] + 12 x bb[2] - 56 x bb[1] + 56 x bb[0] - \par \par 4 5 7 5 6 \par 16 x bb[3] + 32 x bb[2] - 32 x bb[0] + 12 x bb[3] - 56 x bb[2] + \par \par 7 8 6 8 9 \par 56 x bb[1] - 12 x bb[0] + 32 x bb[3] - 32 x bb[1] + 16 x bb[0] - \par \par 7 8 9 10 9 \par 56 x bb[3] + 56 x bb[2] - 12 x bb[1] - 4 x bb[0] - 32 x bb[2] + \par \par 10 9 10 11 10 \par 16 x bb[1] + 56 x bb[3] - 12 x bb[2] - 4 x bb[1] - 32 x bb[3] + \par \par 11 11 12 12 13 \par 16 x bb[2] - 12 x bb[3] - 4 x bb[2] + 16 x bb[3] - 4 x bb[3] + \par \par 2 4 \par 4 aa[0] + aa[1] + 4 bb[0] + 4 x + 4 x - 4 \par \par \pard\ri4\plain\f2\fs22\cf0 13. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}nops(s) \par \pard\li50\ri6\plain\f3\fs22\cf2\protect {\pict\wmetafile8\picw776\pich827\picwgoal439\pichgoal468 0100090000031E01000005001C0000000000050000000B0200000000050000000C023B03080303 0000001E00030000001E00050000000C02D501B801050000000B020000000014000000FF060000 0600F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D0100 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\pard\ri4\plain\f2\fs22\cf0 14. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}sol:=solve(\{coeff(s,x,i) $ i=0..degree(s,x)\},\{aa[k] $ k=0..degree(b,x)-1\} union \{bb[k] $ k=0..degree(d,x)-1\}) \par \pard\li50\ri6\plain\f3\fs22\cf2\protect {\pict\wmetafile8\picw29729\pich1139\picwgoal16854\pichgoal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0000F0010D0004000000F0010E0004000000F0010F0004000000F001100004000000F001110004 000000F001120004000000F0011300040000002701FFFF030000000000 }\plain\f3\fs22\cf2\protect \par \pard\li50\ri2\plain\f3\fs22\cf2\protect \par \pard\ri4\plain\f2\fs22\cf0 19. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}RationaleZerlegung:=proc(r,x) \par \pard\li600\ri1\fi-300\plain\f3\fs22\cf1 local p,q,Pol,a,b,c,d,s,sol; \par begin \par p:=numer(r); \par q:=denom(r); \par Pol:=divide(p,q,[x],Quo); \par p:=divide(p,q,[x],Rem); \par b:=gcd(q,diff(q,x)); \par d:=normal(q/b); \par a:=_plus(aa[k]*x^k $ k=0..degree(b,x)-1); \par c:=_plus(bb[k]*x^k $ k=0..degree(d,x)-1); \par s:=normal(p-q*(diff(a/b,x)+c/d)); \par sol:=solve(\{coeff(s,x,i) $ i=0..degree(s,x)\},\{aa[k] $ k=0..degree(b,x)-1\} union \{bb[k] $ k=0..degree(d,x)-1\}); \par a:=subs(a,sol[1]); \par c:=subs(c,sol[1]); \par [int(Pol,x)+normal(a/b),normal(c/d)] \par end_proc: \par 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