Optimal. Leaf size=262 \[ \frac {120 d^3 (b c-a d)^7 x}{b^{10}}-\frac {(b c-a d)^{10}}{2 b^{11} (a+b x)^2}-\frac {10 d (b c-a d)^9}{b^{11} (a+b x)}+\frac {105 d^4 (b c-a d)^6 (a+b x)^2}{b^{11}}+\frac {84 d^5 (b c-a d)^5 (a+b x)^3}{b^{11}}+\frac {105 d^6 (b c-a d)^4 (a+b x)^4}{2 b^{11}}+\frac {24 d^7 (b c-a d)^3 (a+b x)^5}{b^{11}}+\frac {15 d^8 (b c-a d)^2 (a+b x)^6}{2 b^{11}}+\frac {10 d^9 (b c-a d) (a+b x)^7}{7 b^{11}}+\frac {d^{10} (a+b x)^8}{8 b^{11}}+\frac {45 d^2 (b c-a d)^8 \log (a+b x)}{b^{11}} \]
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Rubi [A]
time = 0.31, antiderivative size = 262, 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 {10 d^9 (a+b x)^7 (b c-a d)}{7 b^{11}}+\frac {15 d^8 (a+b x)^6 (b c-a d)^2}{2 b^{11}}+\frac {24 d^7 (a+b x)^5 (b c-a d)^3}{b^{11}}+\frac {105 d^6 (a+b x)^4 (b c-a d)^4}{2 b^{11}}+\frac {84 d^5 (a+b x)^3 (b c-a d)^5}{b^{11}}+\frac {105 d^4 (a+b x)^2 (b c-a d)^6}{b^{11}}+\frac {45 d^2 (b c-a d)^8 \log (a+b x)}{b^{11}}-\frac {10 d (b c-a d)^9}{b^{11} (a+b x)}-\frac {(b c-a d)^{10}}{2 b^{11} (a+b x)^2}+\frac {d^{10} (a+b x)^8}{8 b^{11}}+\frac {120 d^3 x (b c-a d)^7}{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)^3} \, dx &=\int \left (\frac {120 d^3 (b c-a d)^7}{b^{10}}+\frac {(b c-a d)^{10}}{b^{10} (a+b x)^3}+\frac {10 d (b c-a d)^9}{b^{10} (a+b x)^2}+\frac {45 d^2 (b c-a d)^8}{b^{10} (a+b x)}+\frac {210 d^4 (b c-a d)^6 (a+b x)}{b^{10}}+\frac {252 d^5 (b c-a d)^5 (a+b x)^2}{b^{10}}+\frac {210 d^6 (b c-a d)^4 (a+b x)^3}{b^{10}}+\frac {120 d^7 (b c-a d)^3 (a+b x)^4}{b^{10}}+\frac {45 d^8 (b c-a d)^2 (a+b x)^5}{b^{10}}+\frac {10 d^9 (b c-a d) (a+b x)^6}{b^{10}}+\frac {d^{10} (a+b x)^7}{b^{10}}\right ) \, dx\\ &=\frac {120 d^3 (b c-a d)^7 x}{b^{10}}-\frac {(b c-a d)^{10}}{2 b^{11} (a+b x)^2}-\frac {10 d (b c-a d)^9}{b^{11} (a+b x)}+\frac {105 d^4 (b c-a d)^6 (a+b x)^2}{b^{11}}+\frac {84 d^5 (b c-a d)^5 (a+b x)^3}{b^{11}}+\frac {105 d^6 (b c-a d)^4 (a+b x)^4}{2 b^{11}}+\frac {24 d^7 (b c-a d)^3 (a+b x)^5}{b^{11}}+\frac {15 d^8 (b c-a d)^2 (a+b x)^6}{2 b^{11}}+\frac {10 d^9 (b c-a d) (a+b x)^7}{7 b^{11}}+\frac {d^{10} (a+b x)^8}{8 b^{11}}+\frac {45 d^2 (b c-a d)^8 \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. \(2(262)=524\).
time = 0.16, size = 708, normalized size = 2.70 \begin {gather*} \frac {532 a^{10} d^{10}-56 a^9 b d^9 (85 c+26 d x)+28 a^8 b^2 d^8 \left (675 c^2+380 c d x-116 d^2 x^2\right )-280 a^7 b^3 d^7 \left (156 c^3+117 c^2 d x-91 c d^2 x^2+3 d^3 x^3\right )+210 a^6 b^4 d^6 \left (308 c^4+256 c^3 d x-414 c^2 d^2 x^2+32 c d^3 x^3+d^4 x^4\right )-84 a^5 b^5 d^5 \left (756 c^5+560 c^4 d x-2000 c^3 d^2 x^2+280 c^2 d^3 x^3+20 c d^4 x^4+d^5 x^5\right )+42 a^4 b^6 d^4 \left (980 c^6+336 c^5 d x-4760 c^4 d^2 x^2+1120 c^3 d^3 x^3+140 c^2 d^4 x^4+16 c d^5 x^5+d^6 x^6\right )-24 a^3 b^7 d^3 \left (700 c^7-490 c^6 d x-6174 c^5 d^2 x^2+2450 c^4 d^3 x^3+490 c^3 d^4 x^4+98 c^2 d^5 x^5+14 c d^6 x^6+d^7 x^7\right )+3 a^2 b^8 d^2 \left (1260 c^8-4480 c^7 d x-21560 c^6 d^2 x^2+15680 c^5 d^3 x^3+4900 c^4 d^4 x^4+1568 c^3 d^5 x^5+392 c^2 d^6 x^6+64 c d^7 x^7+5 d^8 x^8\right )-2 a b^9 d \left (140 c^9-2520 c^8 d x-6720 c^7 d^2 x^2+11760 c^6 d^3 x^3+5880 c^5 d^4 x^4+2940 c^4 d^5 x^5+1176 c^3 d^6 x^6+336 c^2 d^7 x^7+60 c d^8 x^8+5 d^9 x^9\right )+b^{10} \left (-28 c^{10}-560 c^9 d x+6720 c^7 d^3 x^3+5880 c^6 d^4 x^4+4704 c^5 d^5 x^5+2940 c^4 d^6 x^6+1344 c^3 d^7 x^7+420 c^2 d^8 x^8+80 c d^9 x^9+7 d^{10} x^{10}\right )+2520 d^2 (b c-a d)^8 (a+b x)^2 \log (a+b x)}{56 b^{11} (a+b x)^2} \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. \(913\) vs.
\(2(252)=504\).
time = 0.16, size = 914, normalized size = 3.49 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. 881 vs.
\(2 (252) = 504\).
time = 0.29, size = 881, normalized size = 3.36 \begin {gather*} -\frac {b^{10} c^{10} + 10 \, a b^{9} c^{9} d - 135 \, a^{2} b^{8} c^{8} d^{2} + 600 \, a^{3} b^{7} c^{7} d^{3} - 1470 \, a^{4} b^{6} c^{6} d^{4} + 2268 \, a^{5} b^{5} c^{5} d^{5} - 2310 \, a^{6} b^{4} c^{4} d^{6} + 1560 \, a^{7} b^{3} c^{3} d^{7} - 675 \, a^{8} b^{2} c^{2} d^{8} + 170 \, a^{9} b c d^{9} - 19 \, a^{10} d^{10} + 20 \, {\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}{2 \, {\left (b^{13} x^{2} + 2 \, a b^{12} x + a^{2} b^{11}\right )}} + \frac {7 \, b^{7} d^{10} x^{8} + 8 \, {\left (10 \, b^{7} c d^{9} - 3 \, a b^{6} d^{10}\right )} x^{7} + 28 \, {\left (15 \, b^{7} c^{2} d^{8} - 10 \, a b^{6} c d^{9} + 2 \, a^{2} b^{5} d^{10}\right )} x^{6} + 56 \, {\left (24 \, b^{7} c^{3} d^{7} - 27 \, a b^{6} c^{2} d^{8} + 12 \, a^{2} b^{5} c d^{9} - 2 \, a^{3} b^{4} d^{10}\right )} x^{5} + 70 \, {\left (42 \, b^{7} c^{4} d^{6} - 72 \, a b^{6} c^{3} d^{7} + 54 \, a^{2} b^{5} c^{2} d^{8} - 20 \, a^{3} b^{4} c d^{9} + 3 \, a^{4} b^{3} d^{10}\right )} x^{4} + 56 \, {\left (84 \, b^{7} c^{5} d^{5} - 210 \, a b^{6} c^{4} d^{6} + 240 \, a^{2} b^{5} c^{3} d^{7} - 150 \, a^{3} b^{4} c^{2} d^{8} + 50 \, a^{4} b^{3} c d^{9} - 7 \, a^{5} b^{2} d^{10}\right )} x^{3} + 28 \, {\left (210 \, b^{7} c^{6} d^{4} - 756 \, a b^{6} c^{5} d^{5} + 1260 \, a^{2} b^{5} c^{4} d^{6} - 1200 \, a^{3} b^{4} c^{3} d^{7} + 675 \, a^{4} b^{3} c^{2} d^{8} - 210 \, a^{5} b^{2} c d^{9} + 28 \, a^{6} b d^{10}\right )} x^{2} + 56 \, {\left (120 \, b^{7} c^{7} d^{3} - 630 \, a b^{6} c^{6} d^{4} + 1512 \, a^{2} b^{5} c^{5} d^{5} - 2100 \, a^{3} b^{4} c^{4} d^{6} + 1800 \, a^{4} b^{3} c^{3} d^{7} - 945 \, a^{5} b^{2} c^{2} d^{8} + 280 \, a^{6} b c d^{9} - 36 \, a^{7} d^{10}\right )} x}{56 \, b^{10}} + \frac {45 \, {\left (b^{8} c^{8} d^{2} - 8 \, a b^{7} c^{7} d^{3} + 28 \, a^{2} b^{6} c^{6} d^{4} - 56 \, a^{3} b^{5} c^{5} d^{5} + 70 \, a^{4} b^{4} c^{4} d^{6} - 56 \, a^{5} b^{3} c^{3} d^{7} + 28 \, a^{6} b^{2} c^{2} d^{8} - 8 \, a^{7} b c d^{9} + a^{8} 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. 1233 vs.
\(2 (252) = 504\).
time = 0.58, size = 1233, normalized size = 4.71 \begin {gather*} \frac {7 \, b^{10} d^{10} x^{10} - 28 \, b^{10} c^{10} - 280 \, a b^{9} c^{9} d + 3780 \, a^{2} b^{8} c^{8} d^{2} - 16800 \, a^{3} b^{7} c^{7} d^{3} + 41160 \, a^{4} b^{6} c^{6} d^{4} - 63504 \, a^{5} b^{5} c^{5} d^{5} + 64680 \, a^{6} b^{4} c^{4} d^{6} - 43680 \, a^{7} b^{3} c^{3} d^{7} + 18900 \, a^{8} b^{2} c^{2} d^{8} - 4760 \, a^{9} b c d^{9} + 532 \, a^{10} d^{10} + 10 \, {\left (8 \, b^{10} c d^{9} - a b^{9} d^{10}\right )} x^{9} + 15 \, {\left (28 \, b^{10} c^{2} d^{8} - 8 \, a b^{9} c d^{9} + a^{2} b^{8} d^{10}\right )} x^{8} + 24 \, {\left (56 \, b^{10} c^{3} d^{7} - 28 \, a b^{9} c^{2} d^{8} + 8 \, a^{2} b^{8} c d^{9} - a^{3} b^{7} d^{10}\right )} x^{7} + 42 \, {\left (70 \, b^{10} c^{4} d^{6} - 56 \, a b^{9} c^{3} d^{7} + 28 \, a^{2} b^{8} c^{2} d^{8} - 8 \, a^{3} b^{7} c d^{9} + a^{4} b^{6} d^{10}\right )} x^{6} + 84 \, {\left (56 \, b^{10} c^{5} d^{5} - 70 \, a b^{9} c^{4} d^{6} + 56 \, a^{2} b^{8} c^{3} d^{7} - 28 \, a^{3} b^{7} c^{2} d^{8} + 8 \, a^{4} b^{6} c d^{9} - a^{5} b^{5} d^{10}\right )} x^{5} + 210 \, {\left (28 \, b^{10} c^{6} d^{4} - 56 \, a b^{9} c^{5} d^{5} + 70 \, a^{2} b^{8} c^{4} d^{6} - 56 \, a^{3} b^{7} c^{3} d^{7} + 28 \, a^{4} b^{6} c^{2} d^{8} - 8 \, a^{5} b^{5} c d^{9} + a^{6} b^{4} d^{10}\right )} x^{4} + 840 \, {\left (8 \, b^{10} c^{7} d^{3} - 28 \, a b^{9} c^{6} d^{4} + 56 \, a^{2} b^{8} c^{5} d^{5} - 70 \, a^{3} b^{7} c^{4} d^{6} + 56 \, a^{4} b^{6} c^{3} d^{7} - 28 \, a^{5} b^{5} c^{2} d^{8} + 8 \, a^{6} b^{4} c d^{9} - a^{7} b^{3} d^{10}\right )} x^{3} + 28 \, {\left (480 \, a b^{9} c^{7} d^{3} - 2310 \, a^{2} b^{8} c^{6} d^{4} + 5292 \, a^{3} b^{7} c^{5} d^{5} - 7140 \, a^{4} b^{6} c^{4} d^{6} + 6000 \, a^{5} b^{5} c^{3} d^{7} - 3105 \, a^{6} b^{4} c^{2} d^{8} + 910 \, a^{7} b^{3} c d^{9} - 116 \, a^{8} b^{2} d^{10}\right )} x^{2} - 56 \, {\left (10 \, b^{10} c^{9} d - 90 \, a b^{9} c^{8} d^{2} + 240 \, a^{2} b^{8} c^{7} d^{3} - 210 \, a^{3} b^{7} c^{6} d^{4} - 252 \, a^{4} b^{6} c^{5} d^{5} + 840 \, a^{5} b^{5} c^{4} d^{6} - 960 \, a^{6} b^{4} c^{3} d^{7} + 585 \, a^{7} b^{3} c^{2} d^{8} - 190 \, a^{8} b^{2} c d^{9} + 26 \, a^{9} b d^{10}\right )} x + 2520 \, {\left (a^{2} b^{8} c^{8} d^{2} - 8 \, a^{3} b^{7} c^{7} d^{3} + 28 \, a^{4} b^{6} c^{6} d^{4} - 56 \, a^{5} b^{5} c^{5} d^{5} + 70 \, a^{6} b^{4} c^{4} d^{6} - 56 \, a^{7} b^{3} c^{3} d^{7} + 28 \, a^{8} b^{2} c^{2} d^{8} - 8 \, a^{9} b c d^{9} + a^{10} d^{10} + {\left (b^{10} c^{8} d^{2} - 8 \, a b^{9} c^{7} d^{3} + 28 \, a^{2} b^{8} c^{6} d^{4} - 56 \, a^{3} b^{7} c^{5} d^{5} + 70 \, a^{4} b^{6} c^{4} d^{6} - 56 \, a^{5} b^{5} c^{3} d^{7} + 28 \, a^{6} b^{4} c^{2} d^{8} - 8 \, a^{7} b^{3} c d^{9} + a^{8} b^{2} d^{10}\right )} x^{2} + 2 \, {\left (a b^{9} c^{8} d^{2} - 8 \, a^{2} b^{8} c^{7} d^{3} + 28 \, a^{3} b^{7} c^{6} d^{4} - 56 \, a^{4} b^{6} c^{5} d^{5} + 70 \, a^{5} b^{5} c^{4} d^{6} - 56 \, a^{6} b^{4} c^{3} d^{7} + 28 \, a^{7} b^{3} c^{2} d^{8} - 8 \, a^{8} b^{2} c d^{9} + a^{9} b d^{10}\right )} x\right )} \log \left (b x + a\right )}{56 \, {\left (b^{13} x^{2} + 2 \, a b^{12} x + a^{2} 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. 843 vs.
\(2 (243) = 486\).
time = 6.27, size = 843, normalized size = 3.22 \begin {gather*} x^{7} \left (- \frac {3 a d^{10}}{7 b^{4}} + \frac {10 c d^{9}}{7 b^{3}}\right ) + x^{6} \left (\frac {a^{2} d^{10}}{b^{5}} - \frac {5 a c d^{9}}{b^{4}} + \frac {15 c^{2} d^{8}}{2 b^{3}}\right ) + x^{5} \left (- \frac {2 a^{3} d^{10}}{b^{6}} + \frac {12 a^{2} c d^{9}}{b^{5}} - \frac {27 a c^{2} d^{8}}{b^{4}} + \frac {24 c^{3} d^{7}}{b^{3}}\right ) + x^{4} \cdot \left (\frac {15 a^{4} d^{10}}{4 b^{7}} - \frac {25 a^{3} c d^{9}}{b^{6}} + \frac {135 a^{2} c^{2} d^{8}}{2 b^{5}} - \frac {90 a c^{3} d^{7}}{b^{4}} + \frac {105 c^{4} d^{6}}{2 b^{3}}\right ) + x^{3} \left (- \frac {7 a^{5} d^{10}}{b^{8}} + \frac {50 a^{4} c d^{9}}{b^{7}} - \frac {150 a^{3} c^{2} d^{8}}{b^{6}} + \frac {240 a^{2} c^{3} d^{7}}{b^{5}} - \frac {210 a c^{4} d^{6}}{b^{4}} + \frac {84 c^{5} d^{5}}{b^{3}}\right ) + x^{2} \cdot \left (\frac {14 a^{6} d^{10}}{b^{9}} - \frac {105 a^{5} c d^{9}}{b^{8}} + \frac {675 a^{4} c^{2} d^{8}}{2 b^{7}} - \frac {600 a^{3} c^{3} d^{7}}{b^{6}} + \frac {630 a^{2} c^{4} d^{6}}{b^{5}} - \frac {378 a c^{5} d^{5}}{b^{4}} + \frac {105 c^{6} d^{4}}{b^{3}}\right ) + x \left (- \frac {36 a^{7} d^{10}}{b^{10}} + \frac {280 a^{6} c d^{9}}{b^{9}} - \frac {945 a^{5} c^{2} d^{8}}{b^{8}} + \frac {1800 a^{4} c^{3} d^{7}}{b^{7}} - \frac {2100 a^{3} c^{4} d^{6}}{b^{6}} + \frac {1512 a^{2} c^{5} d^{5}}{b^{5}} - \frac {630 a c^{6} d^{4}}{b^{4}} + \frac {120 c^{7} d^{3}}{b^{3}}\right ) + \frac {19 a^{10} d^{10} - 170 a^{9} b c d^{9} + 675 a^{8} b^{2} c^{2} d^{8} - 1560 a^{7} b^{3} c^{3} d^{7} + 2310 a^{6} b^{4} c^{4} d^{6} - 2268 a^{5} b^{5} c^{5} d^{5} + 1470 a^{4} b^{6} c^{6} d^{4} - 600 a^{3} b^{7} c^{7} d^{3} + 135 a^{2} b^{8} c^{8} d^{2} - 10 a b^{9} c^{9} d - b^{10} c^{10} + x \left (20 a^{9} b d^{10} - 180 a^{8} b^{2} c d^{9} + 720 a^{7} b^{3} c^{2} d^{8} - 1680 a^{6} b^{4} c^{3} d^{7} + 2520 a^{5} b^{5} c^{4} d^{6} - 2520 a^{4} b^{6} c^{5} d^{5} + 1680 a^{3} b^{7} c^{6} d^{4} - 720 a^{2} b^{8} c^{7} d^{3} + 180 a b^{9} c^{8} d^{2} - 20 b^{10} c^{9} d\right )}{2 a^{2} b^{11} + 4 a b^{12} x + 2 b^{13} x^{2}} + \frac {d^{10} x^{8}}{8 b^{3}} + \frac {45 d^{2} \left (a d - b c\right )^{8} \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. 924 vs.
\(2 (252) = 504\).
time = 0.61, size = 924, normalized size = 3.53 \begin {gather*} \frac {45 \, {\left (b^{8} c^{8} d^{2} - 8 \, a b^{7} c^{7} d^{3} + 28 \, a^{2} b^{6} c^{6} d^{4} - 56 \, a^{3} b^{5} c^{5} d^{5} + 70 \, a^{4} b^{4} c^{4} d^{6} - 56 \, a^{5} b^{3} c^{3} d^{7} + 28 \, a^{6} b^{2} c^{2} d^{8} - 8 \, a^{7} b c d^{9} + a^{8} d^{10}\right )} \log \left ({\left | b x + a \right |}\right )}{b^{11}} - \frac {b^{10} c^{10} + 10 \, a b^{9} c^{9} d - 135 \, a^{2} b^{8} c^{8} d^{2} + 600 \, a^{3} b^{7} c^{7} d^{3} - 1470 \, a^{4} b^{6} c^{6} d^{4} + 2268 \, a^{5} b^{5} c^{5} d^{5} - 2310 \, a^{6} b^{4} c^{4} d^{6} + 1560 \, a^{7} b^{3} c^{3} d^{7} - 675 \, a^{8} b^{2} c^{2} d^{8} + 170 \, a^{9} b c d^{9} - 19 \, a^{10} d^{10} + 20 \, {\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}{2 \, {\left (b x + a\right )}^{2} b^{11}} + \frac {7 \, b^{21} d^{10} x^{8} + 80 \, b^{21} c d^{9} x^{7} - 24 \, a b^{20} d^{10} x^{7} + 420 \, b^{21} c^{2} d^{8} x^{6} - 280 \, a b^{20} c d^{9} x^{6} + 56 \, a^{2} b^{19} d^{10} x^{6} + 1344 \, b^{21} c^{3} d^{7} x^{5} - 1512 \, a b^{20} c^{2} d^{8} x^{5} + 672 \, a^{2} b^{19} c d^{9} x^{5} - 112 \, a^{3} b^{18} d^{10} x^{5} + 2940 \, b^{21} c^{4} d^{6} x^{4} - 5040 \, a b^{20} c^{3} d^{7} x^{4} + 3780 \, a^{2} b^{19} c^{2} d^{8} x^{4} - 1400 \, a^{3} b^{18} c d^{9} x^{4} + 210 \, a^{4} b^{17} d^{10} x^{4} + 4704 \, b^{21} c^{5} d^{5} x^{3} - 11760 \, a b^{20} c^{4} d^{6} x^{3} + 13440 \, a^{2} b^{19} c^{3} d^{7} x^{3} - 8400 \, a^{3} b^{18} c^{2} d^{8} x^{3} + 2800 \, a^{4} b^{17} c d^{9} x^{3} - 392 \, a^{5} b^{16} d^{10} x^{3} + 5880 \, b^{21} c^{6} d^{4} x^{2} - 21168 \, a b^{20} c^{5} d^{5} x^{2} + 35280 \, a^{2} b^{19} c^{4} d^{6} x^{2} - 33600 \, a^{3} b^{18} c^{3} d^{7} x^{2} + 18900 \, a^{4} b^{17} c^{2} d^{8} x^{2} - 5880 \, a^{5} b^{16} c d^{9} x^{2} + 784 \, a^{6} b^{15} d^{10} x^{2} + 6720 \, b^{21} c^{7} d^{3} x - 35280 \, a b^{20} c^{6} d^{4} x + 84672 \, a^{2} b^{19} c^{5} d^{5} x - 117600 \, a^{3} b^{18} c^{4} d^{6} x + 100800 \, a^{4} b^{17} c^{3} d^{7} x - 52920 \, a^{5} b^{16} c^{2} d^{8} x + 15680 \, a^{6} b^{15} c d^{9} x - 2016 \, a^{7} b^{14} d^{10} x}{56 \, b^{24}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.38, size = 2500, normalized size = 9.54 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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