Optimal. Leaf size=258 \[ \frac {45 d^2 (b c-a d)^8 x}{b^{10}}-\frac {(b c-a d)^{10}}{b^{11} (a+b x)}+\frac {60 d^3 (b c-a d)^7 (a+b x)^2}{b^{11}}+\frac {70 d^4 (b c-a d)^6 (a+b x)^3}{b^{11}}+\frac {63 d^5 (b c-a d)^5 (a+b x)^4}{b^{11}}+\frac {42 d^6 (b c-a d)^4 (a+b x)^5}{b^{11}}+\frac {20 d^7 (b c-a d)^3 (a+b x)^6}{b^{11}}+\frac {45 d^8 (b c-a d)^2 (a+b x)^7}{7 b^{11}}+\frac {5 d^9 (b c-a d) (a+b x)^8}{4 b^{11}}+\frac {d^{10} (a+b x)^9}{9 b^{11}}+\frac {10 d (b c-a d)^9 \log (a+b x)}{b^{11}} \]
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Rubi [A]
time = 0.32, antiderivative size = 258, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {45}
\begin {gather*} \frac {5 d^9 (a+b x)^8 (b c-a d)}{4 b^{11}}+\frac {45 d^8 (a+b x)^7 (b c-a d)^2}{7 b^{11}}+\frac {20 d^7 (a+b x)^6 (b c-a d)^3}{b^{11}}+\frac {42 d^6 (a+b x)^5 (b c-a d)^4}{b^{11}}+\frac {63 d^5 (a+b x)^4 (b c-a d)^5}{b^{11}}+\frac {70 d^4 (a+b x)^3 (b c-a d)^6}{b^{11}}+\frac {60 d^3 (a+b x)^2 (b c-a d)^7}{b^{11}}-\frac {(b c-a d)^{10}}{b^{11} (a+b x)}+\frac {10 d (b c-a d)^9 \log (a+b x)}{b^{11}}+\frac {d^{10} (a+b x)^9}{9 b^{11}}+\frac {45 d^2 x (b c-a d)^8}{b^{10}} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int \frac {(c+d x)^{10}}{(a+b x)^2} \, dx &=\int \left (\frac {45 d^2 (b c-a d)^8}{b^{10}}+\frac {(b c-a d)^{10}}{b^{10} (a+b x)^2}+\frac {10 d (b c-a d)^9}{b^{10} (a+b x)}+\frac {120 d^3 (b c-a d)^7 (a+b x)}{b^{10}}+\frac {210 d^4 (b c-a d)^6 (a+b x)^2}{b^{10}}+\frac {252 d^5 (b c-a d)^5 (a+b x)^3}{b^{10}}+\frac {210 d^6 (b c-a d)^4 (a+b x)^4}{b^{10}}+\frac {120 d^7 (b c-a d)^3 (a+b x)^5}{b^{10}}+\frac {45 d^8 (b c-a d)^2 (a+b x)^6}{b^{10}}+\frac {10 d^9 (b c-a d) (a+b x)^7}{b^{10}}+\frac {d^{10} (a+b x)^8}{b^{10}}\right ) \, dx\\ &=\frac {45 d^2 (b c-a d)^8 x}{b^{10}}-\frac {(b c-a d)^{10}}{b^{11} (a+b x)}+\frac {60 d^3 (b c-a d)^7 (a+b x)^2}{b^{11}}+\frac {70 d^4 (b c-a d)^6 (a+b x)^3}{b^{11}}+\frac {63 d^5 (b c-a d)^5 (a+b x)^4}{b^{11}}+\frac {42 d^6 (b c-a d)^4 (a+b x)^5}{b^{11}}+\frac {20 d^7 (b c-a d)^3 (a+b x)^6}{b^{11}}+\frac {45 d^8 (b c-a d)^2 (a+b x)^7}{7 b^{11}}+\frac {5 d^9 (b c-a d) (a+b x)^8}{4 b^{11}}+\frac {d^{10} (a+b x)^9}{9 b^{11}}+\frac {10 d (b c-a d)^9 \log (a+b x)}{b^{11}}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(708\) vs. \(2(258)=516\).
time = 0.17, size = 708, normalized size = 2.74 \begin {gather*} \frac {-252 a^{10} d^{10}+252 a^9 b d^9 (10 c+9 d x)+1260 a^8 b^2 d^8 \left (-9 c^2-16 c d x+d^2 x^2\right )-420 a^7 b^3 d^7 \left (-72 c^3-189 c^2 d x+27 c d^2 x^2+d^3 x^3\right )+210 a^6 b^4 d^6 \left (-252 c^4-864 c^3 d x+216 c^2 d^2 x^2+18 c d^3 x^3+d^4 x^4\right )-126 a^5 b^5 d^5 \left (-504 c^5-2100 c^4 d x+840 c^3 d^2 x^2+120 c^2 d^3 x^3+15 c d^4 x^4+d^5 x^5\right )+42 a^4 b^6 d^4 \left (-1260 c^6-6048 c^5 d x+3780 c^4 d^2 x^2+840 c^3 d^3 x^3+180 c^2 d^4 x^4+27 c d^5 x^5+2 d^6 x^6\right )-12 a^3 b^7 d^3 \left (-2520 c^7-13230 c^6 d x+13230 c^5 d^2 x^2+4410 c^4 d^3 x^3+1470 c^3 d^4 x^4+378 c^2 d^5 x^5+63 c d^6 x^6+5 d^7 x^7\right )+9 a^2 b^8 d^2 \left (-1260 c^8-6720 c^7 d x+11760 c^6 d^2 x^2+5880 c^5 d^3 x^3+2940 c^4 d^4 x^4+1176 c^3 d^5 x^5+336 c^2 d^6 x^6+60 c d^7 x^7+5 d^8 x^8\right )-a b^9 d \left (-2520 c^9-11340 c^8 d x+45360 c^7 d^2 x^2+35280 c^6 d^3 x^3+26460 c^5 d^4 x^4+15876 c^4 d^5 x^5+7056 c^3 d^6 x^6+2160 c^2 d^7 x^7+405 c d^8 x^8+35 d^9 x^9\right )+b^{10} \left (-252 c^{10}+11340 c^8 d^2 x^2+15120 c^7 d^3 x^3+17640 c^6 d^4 x^4+15876 c^5 d^5 x^5+10584 c^4 d^6 x^6+5040 c^3 d^7 x^7+1620 c^2 d^8 x^8+315 c d^9 x^9+28 d^{10} x^{10}\right )-2520 d (-b c+a d)^9 (a+b x) \log (a+b x)}{252 b^{11} (a+b x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(932\) vs.
\(2(252)=504\).
time = 0.15, size = 933, normalized size = 3.62 Too large to display
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 874 vs.
\(2 (252) = 504\).
time = 0.29, size = 874, normalized size = 3.39 \begin {gather*} -\frac {b^{10} c^{10} - 10 \, a b^{9} c^{9} d + 45 \, a^{2} b^{8} c^{8} d^{2} - 120 \, a^{3} b^{7} c^{7} d^{3} + 210 \, a^{4} b^{6} c^{6} d^{4} - 252 \, a^{5} b^{5} c^{5} d^{5} + 210 \, a^{6} b^{4} c^{4} d^{6} - 120 \, a^{7} b^{3} c^{3} d^{7} + 45 \, a^{8} b^{2} c^{2} d^{8} - 10 \, a^{9} b c d^{9} + a^{10} d^{10}}{b^{12} x + a b^{11}} + \frac {28 \, b^{8} d^{10} x^{9} + 63 \, {\left (5 \, b^{8} c d^{9} - a b^{7} d^{10}\right )} x^{8} + 36 \, {\left (45 \, b^{8} c^{2} d^{8} - 20 \, a b^{7} c d^{9} + 3 \, a^{2} b^{6} d^{10}\right )} x^{7} + 84 \, {\left (60 \, b^{8} c^{3} d^{7} - 45 \, a b^{7} c^{2} d^{8} + 15 \, a^{2} b^{6} c d^{9} - 2 \, a^{3} b^{5} d^{10}\right )} x^{6} + 252 \, {\left (42 \, b^{8} c^{4} d^{6} - 48 \, a b^{7} c^{3} d^{7} + 27 \, a^{2} b^{6} c^{2} d^{8} - 8 \, a^{3} b^{5} c d^{9} + a^{4} b^{4} d^{10}\right )} x^{5} + 126 \, {\left (126 \, b^{8} c^{5} d^{5} - 210 \, a b^{7} c^{4} d^{6} + 180 \, a^{2} b^{6} c^{3} d^{7} - 90 \, a^{3} b^{5} c^{2} d^{8} + 25 \, a^{4} b^{4} c d^{9} - 3 \, a^{5} b^{3} d^{10}\right )} x^{4} + 84 \, {\left (210 \, b^{8} c^{6} d^{4} - 504 \, a b^{7} c^{5} d^{5} + 630 \, a^{2} b^{6} c^{4} d^{6} - 480 \, a^{3} b^{5} c^{3} d^{7} + 225 \, a^{4} b^{4} c^{2} d^{8} - 60 \, a^{5} b^{3} c d^{9} + 7 \, a^{6} b^{2} d^{10}\right )} x^{3} + 252 \, {\left (60 \, b^{8} c^{7} d^{3} - 210 \, a b^{7} c^{6} d^{4} + 378 \, a^{2} b^{6} c^{5} d^{5} - 420 \, a^{3} b^{5} c^{4} d^{6} + 300 \, a^{4} b^{4} c^{3} d^{7} - 135 \, a^{5} b^{3} c^{2} d^{8} + 35 \, a^{6} b^{2} c d^{9} - 4 \, a^{7} b d^{10}\right )} x^{2} + 252 \, {\left (45 \, b^{8} c^{8} d^{2} - 240 \, a b^{7} c^{7} d^{3} + 630 \, a^{2} b^{6} c^{6} d^{4} - 1008 \, a^{3} b^{5} c^{5} d^{5} + 1050 \, a^{4} b^{4} c^{4} d^{6} - 720 \, a^{5} b^{3} c^{3} d^{7} + 315 \, a^{6} b^{2} c^{2} d^{8} - 80 \, a^{7} b c d^{9} + 9 \, a^{8} d^{10}\right )} x}{252 \, b^{10}} + \frac {10 \, {\left (b^{9} c^{9} d - 9 \, a b^{8} c^{8} d^{2} + 36 \, a^{2} b^{7} c^{7} d^{3} - 84 \, a^{3} b^{6} c^{6} d^{4} + 126 \, a^{4} b^{5} c^{5} d^{5} - 126 \, a^{5} b^{4} c^{4} d^{6} + 84 \, a^{6} b^{3} c^{3} d^{7} - 36 \, a^{7} b^{2} c^{2} d^{8} + 9 \, a^{8} b c d^{9} - a^{9} d^{10}\right )} \log \left (b x + a\right )}{b^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 1124 vs.
\(2 (252) = 504\).
time = 0.48, size = 1124, normalized size = 4.36 \begin {gather*} \frac {28 \, b^{10} d^{10} x^{10} - 252 \, b^{10} c^{10} + 2520 \, a b^{9} c^{9} d - 11340 \, a^{2} b^{8} c^{8} d^{2} + 30240 \, a^{3} b^{7} c^{7} d^{3} - 52920 \, a^{4} b^{6} c^{6} d^{4} + 63504 \, a^{5} b^{5} c^{5} d^{5} - 52920 \, a^{6} b^{4} c^{4} d^{6} + 30240 \, a^{7} b^{3} c^{3} d^{7} - 11340 \, a^{8} b^{2} c^{2} d^{8} + 2520 \, a^{9} b c d^{9} - 252 \, a^{10} d^{10} + 35 \, {\left (9 \, b^{10} c d^{9} - a b^{9} d^{10}\right )} x^{9} + 45 \, {\left (36 \, b^{10} c^{2} d^{8} - 9 \, a b^{9} c d^{9} + a^{2} b^{8} d^{10}\right )} x^{8} + 60 \, {\left (84 \, b^{10} c^{3} d^{7} - 36 \, a b^{9} c^{2} d^{8} + 9 \, a^{2} b^{8} c d^{9} - a^{3} b^{7} d^{10}\right )} x^{7} + 84 \, {\left (126 \, b^{10} c^{4} d^{6} - 84 \, a b^{9} c^{3} d^{7} + 36 \, a^{2} b^{8} c^{2} d^{8} - 9 \, a^{3} b^{7} c d^{9} + a^{4} b^{6} d^{10}\right )} x^{6} + 126 \, {\left (126 \, b^{10} c^{5} d^{5} - 126 \, a b^{9} c^{4} d^{6} + 84 \, a^{2} b^{8} c^{3} d^{7} - 36 \, a^{3} b^{7} c^{2} d^{8} + 9 \, a^{4} b^{6} c d^{9} - a^{5} b^{5} d^{10}\right )} x^{5} + 210 \, {\left (84 \, b^{10} c^{6} d^{4} - 126 \, a b^{9} c^{5} d^{5} + 126 \, a^{2} b^{8} c^{4} d^{6} - 84 \, a^{3} b^{7} c^{3} d^{7} + 36 \, a^{4} b^{6} c^{2} d^{8} - 9 \, a^{5} b^{5} c d^{9} + a^{6} b^{4} d^{10}\right )} x^{4} + 420 \, {\left (36 \, b^{10} c^{7} d^{3} - 84 \, a b^{9} c^{6} d^{4} + 126 \, a^{2} b^{8} c^{5} d^{5} - 126 \, a^{3} b^{7} c^{4} d^{6} + 84 \, a^{4} b^{6} c^{3} d^{7} - 36 \, a^{5} b^{5} c^{2} d^{8} + 9 \, a^{6} b^{4} c d^{9} - a^{7} b^{3} d^{10}\right )} x^{3} + 1260 \, {\left (9 \, b^{10} c^{8} d^{2} - 36 \, a b^{9} c^{7} d^{3} + 84 \, a^{2} b^{8} c^{6} d^{4} - 126 \, a^{3} b^{7} c^{5} d^{5} + 126 \, a^{4} b^{6} c^{4} d^{6} - 84 \, a^{5} b^{5} c^{3} d^{7} + 36 \, a^{6} b^{4} c^{2} d^{8} - 9 \, a^{7} b^{3} c d^{9} + a^{8} b^{2} d^{10}\right )} x^{2} + 252 \, {\left (45 \, a b^{9} c^{8} d^{2} - 240 \, a^{2} b^{8} c^{7} d^{3} + 630 \, a^{3} b^{7} c^{6} d^{4} - 1008 \, a^{4} b^{6} c^{5} d^{5} + 1050 \, a^{5} b^{5} c^{4} d^{6} - 720 \, a^{6} b^{4} c^{3} d^{7} + 315 \, a^{7} b^{3} c^{2} d^{8} - 80 \, a^{8} b^{2} c d^{9} + 9 \, a^{9} b d^{10}\right )} x + 2520 \, {\left (a b^{9} c^{9} d - 9 \, a^{2} b^{8} c^{8} d^{2} + 36 \, a^{3} b^{7} c^{7} d^{3} - 84 \, a^{4} b^{6} c^{6} d^{4} + 126 \, a^{5} b^{5} c^{5} d^{5} - 126 \, a^{6} b^{4} c^{4} d^{6} + 84 \, a^{7} b^{3} c^{3} d^{7} - 36 \, a^{8} b^{2} c^{2} d^{8} + 9 \, a^{9} b c d^{9} - a^{10} d^{10} + {\left (b^{10} c^{9} d - 9 \, a b^{9} c^{8} d^{2} + 36 \, a^{2} b^{8} c^{7} d^{3} - 84 \, a^{3} b^{7} c^{6} d^{4} + 126 \, a^{4} b^{6} c^{5} d^{5} - 126 \, a^{5} b^{5} c^{4} d^{6} + 84 \, a^{6} b^{4} c^{3} d^{7} - 36 \, a^{7} b^{3} c^{2} d^{8} + 9 \, a^{8} b^{2} c d^{9} - a^{9} b d^{10}\right )} x\right )} \log \left (b x + a\right )}{252 \, {\left (b^{12} x + a b^{11}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 816 vs.
\(2 (240) = 480\).
time = 1.42, size = 816, normalized size = 3.16 \begin {gather*} x^{8} \left (- \frac {a d^{10}}{4 b^{3}} + \frac {5 c d^{9}}{4 b^{2}}\right ) + x^{7} \cdot \left (\frac {3 a^{2} d^{10}}{7 b^{4}} - \frac {20 a c d^{9}}{7 b^{3}} + \frac {45 c^{2} d^{8}}{7 b^{2}}\right ) + x^{6} \left (- \frac {2 a^{3} d^{10}}{3 b^{5}} + \frac {5 a^{2} c d^{9}}{b^{4}} - \frac {15 a c^{2} d^{8}}{b^{3}} + \frac {20 c^{3} d^{7}}{b^{2}}\right ) + x^{5} \left (\frac {a^{4} d^{10}}{b^{6}} - \frac {8 a^{3} c d^{9}}{b^{5}} + \frac {27 a^{2} c^{2} d^{8}}{b^{4}} - \frac {48 a c^{3} d^{7}}{b^{3}} + \frac {42 c^{4} d^{6}}{b^{2}}\right ) + x^{4} \left (- \frac {3 a^{5} d^{10}}{2 b^{7}} + \frac {25 a^{4} c d^{9}}{2 b^{6}} - \frac {45 a^{3} c^{2} d^{8}}{b^{5}} + \frac {90 a^{2} c^{3} d^{7}}{b^{4}} - \frac {105 a c^{4} d^{6}}{b^{3}} + \frac {63 c^{5} d^{5}}{b^{2}}\right ) + x^{3} \cdot \left (\frac {7 a^{6} d^{10}}{3 b^{8}} - \frac {20 a^{5} c d^{9}}{b^{7}} + \frac {75 a^{4} c^{2} d^{8}}{b^{6}} - \frac {160 a^{3} c^{3} d^{7}}{b^{5}} + \frac {210 a^{2} c^{4} d^{6}}{b^{4}} - \frac {168 a c^{5} d^{5}}{b^{3}} + \frac {70 c^{6} d^{4}}{b^{2}}\right ) + x^{2} \left (- \frac {4 a^{7} d^{10}}{b^{9}} + \frac {35 a^{6} c d^{9}}{b^{8}} - \frac {135 a^{5} c^{2} d^{8}}{b^{7}} + \frac {300 a^{4} c^{3} d^{7}}{b^{6}} - \frac {420 a^{3} c^{4} d^{6}}{b^{5}} + \frac {378 a^{2} c^{5} d^{5}}{b^{4}} - \frac {210 a c^{6} d^{4}}{b^{3}} + \frac {60 c^{7} d^{3}}{b^{2}}\right ) + x \left (\frac {9 a^{8} d^{10}}{b^{10}} - \frac {80 a^{7} c d^{9}}{b^{9}} + \frac {315 a^{6} c^{2} d^{8}}{b^{8}} - \frac {720 a^{5} c^{3} d^{7}}{b^{7}} + \frac {1050 a^{4} c^{4} d^{6}}{b^{6}} - \frac {1008 a^{3} c^{5} d^{5}}{b^{5}} + \frac {630 a^{2} c^{6} d^{4}}{b^{4}} - \frac {240 a c^{7} d^{3}}{b^{3}} + \frac {45 c^{8} d^{2}}{b^{2}}\right ) + \frac {- a^{10} d^{10} + 10 a^{9} b c d^{9} - 45 a^{8} b^{2} c^{2} d^{8} + 120 a^{7} b^{3} c^{3} d^{7} - 210 a^{6} b^{4} c^{4} d^{6} + 252 a^{5} b^{5} c^{5} d^{5} - 210 a^{4} b^{6} c^{6} d^{4} + 120 a^{3} b^{7} c^{7} d^{3} - 45 a^{2} b^{8} c^{8} d^{2} + 10 a b^{9} c^{9} d - b^{10} c^{10}}{a b^{11} + b^{12} x} + \frac {d^{10} x^{9}}{9 b^{2}} - \frac {10 d \left (a d - b c\right )^{9} \log {\left (a + b x \right )}}{b^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 1012 vs.
\(2 (252) = 504\).
time = 0.58, size = 1012, normalized size = 3.92 \begin {gather*} \frac {{\left (28 \, d^{10} + \frac {315 \, {\left (b^{2} c d^{9} - a b d^{10}\right )}}{{\left (b x + a\right )} b} + \frac {1620 \, {\left (b^{4} c^{2} d^{8} - 2 \, a b^{3} c d^{9} + a^{2} b^{2} d^{10}\right )}}{{\left (b x + a\right )}^{2} b^{2}} + \frac {5040 \, {\left (b^{6} c^{3} d^{7} - 3 \, a b^{5} c^{2} d^{8} + 3 \, a^{2} b^{4} c d^{9} - a^{3} b^{3} d^{10}\right )}}{{\left (b x + a\right )}^{3} b^{3}} + \frac {10584 \, {\left (b^{8} c^{4} d^{6} - 4 \, a b^{7} c^{3} d^{7} + 6 \, a^{2} b^{6} c^{2} d^{8} - 4 \, a^{3} b^{5} c d^{9} + a^{4} b^{4} d^{10}\right )}}{{\left (b x + a\right )}^{4} b^{4}} + \frac {15876 \, {\left (b^{10} c^{5} d^{5} - 5 \, a b^{9} c^{4} d^{6} + 10 \, a^{2} b^{8} c^{3} d^{7} - 10 \, a^{3} b^{7} c^{2} d^{8} + 5 \, a^{4} b^{6} c d^{9} - a^{5} b^{5} d^{10}\right )}}{{\left (b x + a\right )}^{5} b^{5}} + \frac {17640 \, {\left (b^{12} c^{6} d^{4} - 6 \, a b^{11} c^{5} d^{5} + 15 \, a^{2} b^{10} c^{4} d^{6} - 20 \, a^{3} b^{9} c^{3} d^{7} + 15 \, a^{4} b^{8} c^{2} d^{8} - 6 \, a^{5} b^{7} c d^{9} + a^{6} b^{6} d^{10}\right )}}{{\left (b x + a\right )}^{6} b^{6}} + \frac {15120 \, {\left (b^{14} c^{7} d^{3} - 7 \, a b^{13} c^{6} d^{4} + 21 \, a^{2} b^{12} c^{5} d^{5} - 35 \, a^{3} b^{11} c^{4} d^{6} + 35 \, a^{4} b^{10} c^{3} d^{7} - 21 \, a^{5} b^{9} c^{2} d^{8} + 7 \, a^{6} b^{8} c d^{9} - a^{7} b^{7} d^{10}\right )}}{{\left (b x + a\right )}^{7} b^{7}} + \frac {11340 \, {\left (b^{16} c^{8} d^{2} - 8 \, a b^{15} c^{7} d^{3} + 28 \, a^{2} b^{14} c^{6} d^{4} - 56 \, a^{3} b^{13} c^{5} d^{5} + 70 \, a^{4} b^{12} c^{4} d^{6} - 56 \, a^{5} b^{11} c^{3} d^{7} + 28 \, a^{6} b^{10} c^{2} d^{8} - 8 \, a^{7} b^{9} c d^{9} + a^{8} b^{8} d^{10}\right )}}{{\left (b x + a\right )}^{8} b^{8}}\right )} {\left (b x + a\right )}^{9}}{252 \, b^{11}} - \frac {10 \, {\left (b^{9} c^{9} d - 9 \, a b^{8} c^{8} d^{2} + 36 \, a^{2} b^{7} c^{7} d^{3} - 84 \, a^{3} b^{6} c^{6} d^{4} + 126 \, a^{4} b^{5} c^{5} d^{5} - 126 \, a^{5} b^{4} c^{4} d^{6} + 84 \, a^{6} b^{3} c^{3} d^{7} - 36 \, a^{7} b^{2} c^{2} d^{8} + 9 \, a^{8} b c d^{9} - a^{9} d^{10}\right )} \log \left (\frac {{\left | b x + a \right |}}{{\left (b x + a\right )}^{2} {\left | b \right |}}\right )}{b^{11}} - \frac {\frac {b^{19} c^{10}}{b x + a} - \frac {10 \, a b^{18} c^{9} d}{b x + a} + \frac {45 \, a^{2} b^{17} c^{8} d^{2}}{b x + a} - \frac {120 \, a^{3} b^{16} c^{7} d^{3}}{b x + a} + \frac {210 \, a^{4} b^{15} c^{6} d^{4}}{b x + a} - \frac {252 \, a^{5} b^{14} c^{5} d^{5}}{b x + a} + \frac {210 \, a^{6} b^{13} c^{4} d^{6}}{b x + a} - \frac {120 \, a^{7} b^{12} c^{3} d^{7}}{b x + a} + \frac {45 \, a^{8} b^{11} c^{2} d^{8}}{b x + a} - \frac {10 \, a^{9} b^{10} c d^{9}}{b x + a} + \frac {a^{10} b^{9} d^{10}}{b x + a}}{b^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.35, size = 2500, normalized size = 9.69 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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