Optimal. Leaf size=262 \[ \frac {120 d^7 (b c-a d)^3 x}{b^{10}}-\frac {(b c-a d)^{10}}{6 b^{11} (a+b x)^6}-\frac {2 d (b c-a d)^9}{b^{11} (a+b x)^5}-\frac {45 d^2 (b c-a d)^8}{4 b^{11} (a+b x)^4}-\frac {40 d^3 (b c-a d)^7}{b^{11} (a+b x)^3}-\frac {105 d^4 (b c-a d)^6}{b^{11} (a+b x)^2}-\frac {252 d^5 (b c-a d)^5}{b^{11} (a+b x)}+\frac {45 d^8 (b c-a d)^2 (a+b x)^2}{2 b^{11}}+\frac {10 d^9 (b c-a d) (a+b x)^3}{3 b^{11}}+\frac {d^{10} (a+b x)^4}{4 b^{11}}+\frac {210 d^6 (b c-a d)^4 \log (a+b x)}{b^{11}} \]
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Rubi [A]
time = 0.27, 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)^3 (b c-a d)}{3 b^{11}}+\frac {45 d^8 (a+b x)^2 (b c-a d)^2}{2 b^{11}}+\frac {210 d^6 (b c-a d)^4 \log (a+b x)}{b^{11}}-\frac {252 d^5 (b c-a d)^5}{b^{11} (a+b x)}-\frac {105 d^4 (b c-a d)^6}{b^{11} (a+b x)^2}-\frac {40 d^3 (b c-a d)^7}{b^{11} (a+b x)^3}-\frac {45 d^2 (b c-a d)^8}{4 b^{11} (a+b x)^4}-\frac {2 d (b c-a d)^9}{b^{11} (a+b x)^5}-\frac {(b c-a d)^{10}}{6 b^{11} (a+b x)^6}+\frac {d^{10} (a+b x)^4}{4 b^{11}}+\frac {120 d^7 x (b c-a d)^3}{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)^7} \, dx &=\int \left (\frac {120 d^7 (b c-a d)^3}{b^{10}}+\frac {(b c-a d)^{10}}{b^{10} (a+b x)^7}+\frac {10 d (b c-a d)^9}{b^{10} (a+b x)^6}+\frac {45 d^2 (b c-a d)^8}{b^{10} (a+b x)^5}+\frac {120 d^3 (b c-a d)^7}{b^{10} (a+b x)^4}+\frac {210 d^4 (b c-a d)^6}{b^{10} (a+b x)^3}+\frac {252 d^5 (b c-a d)^5}{b^{10} (a+b x)^2}+\frac {210 d^6 (b c-a d)^4}{b^{10} (a+b x)}+\frac {45 d^8 (b c-a d)^2 (a+b x)}{b^{10}}+\frac {10 d^9 (b c-a d) (a+b x)^2}{b^{10}}+\frac {d^{10} (a+b x)^3}{b^{10}}\right ) \, dx\\ &=\frac {120 d^7 (b c-a d)^3 x}{b^{10}}-\frac {(b c-a d)^{10}}{6 b^{11} (a+b x)^6}-\frac {2 d (b c-a d)^9}{b^{11} (a+b x)^5}-\frac {45 d^2 (b c-a d)^8}{4 b^{11} (a+b x)^4}-\frac {40 d^3 (b c-a d)^7}{b^{11} (a+b x)^3}-\frac {105 d^4 (b c-a d)^6}{b^{11} (a+b x)^2}-\frac {252 d^5 (b c-a d)^5}{b^{11} (a+b x)}+\frac {45 d^8 (b c-a d)^2 (a+b x)^2}{2 b^{11}}+\frac {10 d^9 (b c-a d) (a+b x)^3}{3 b^{11}}+\frac {d^{10} (a+b x)^4}{4 b^{11}}+\frac {210 d^6 (b c-a d)^4 \log (a+b x)}{b^{11}}\\ \end {align*}
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Mathematica [A]
time = 0.14, size = 265, normalized size = 1.01 \begin {gather*} \frac {12 b d^7 \left (120 b^3 c^3-315 a b^2 c^2 d+280 a^2 b c d^2-84 a^3 d^3\right ) x+6 b^2 d^8 \left (45 b^2 c^2-70 a b c d+28 a^2 d^2\right ) x^2+4 b^3 d^9 (10 b c-7 a d) x^3+3 b^4 d^{10} x^4-\frac {2 (b c-a d)^{10}}{(a+b x)^6}+\frac {24 d (-b c+a d)^9}{(a+b x)^5}-\frac {135 d^2 (b c-a d)^8}{(a+b x)^4}+\frac {480 d^3 (-b c+a d)^7}{(a+b x)^3}-\frac {1260 d^4 (b c-a d)^6}{(a+b x)^2}+\frac {3024 d^5 (-b c+a d)^5}{a+b x}+2520 d^6 (b c-a d)^4 \log (a+b x)}{12 b^{11}} \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. \(861\) vs.
\(2(252)=504\).
time = 0.15, size = 862, normalized size = 3.29 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. 925 vs.
\(2 (252) = 504\).
time = 0.40, size = 925, normalized size = 3.53 \begin {gather*} -\frac {2 \, b^{10} c^{10} + 4 \, a b^{9} c^{9} d + 9 \, a^{2} b^{8} c^{8} d^{2} + 24 \, a^{3} b^{7} c^{7} d^{3} + 84 \, a^{4} b^{6} c^{6} d^{4} + 504 \, a^{5} b^{5} c^{5} d^{5} - 6174 \, a^{6} b^{4} c^{4} d^{6} + 16056 \, a^{7} b^{3} c^{3} d^{7} - 18414 \, a^{8} b^{2} c^{2} d^{8} + 10036 \, a^{9} b c d^{9} - 2131 \, a^{10} d^{10} + 3024 \, {\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 )} x^{5} + 1260 \, {\left (b^{10} c^{6} d^{4} + 6 \, a b^{9} c^{5} d^{5} - 45 \, a^{2} b^{8} c^{4} d^{6} + 100 \, a^{3} b^{7} c^{3} d^{7} - 105 \, a^{4} b^{6} c^{2} d^{8} + 54 \, a^{5} b^{5} c d^{9} - 11 \, a^{6} b^{4} d^{10}\right )} x^{4} + 240 \, {\left (2 \, b^{10} c^{7} d^{3} + 7 \, a b^{9} c^{6} d^{4} + 42 \, a^{2} b^{8} c^{5} d^{5} - 385 \, a^{3} b^{7} c^{4} d^{6} + 910 \, a^{4} b^{6} c^{3} d^{7} - 987 \, a^{5} b^{5} c^{2} d^{8} + 518 \, a^{6} b^{4} c d^{9} - 107 \, a^{7} b^{3} d^{10}\right )} x^{3} + 45 \, {\left (3 \, b^{10} c^{8} d^{2} + 8 \, a b^{9} c^{7} d^{3} + 28 \, a^{2} b^{8} c^{6} d^{4} + 168 \, a^{3} b^{7} c^{5} d^{5} - 1750 \, a^{4} b^{6} c^{4} d^{6} + 4312 \, a^{5} b^{5} c^{3} d^{7} - 4788 \, a^{6} b^{4} c^{2} d^{8} + 2552 \, a^{7} b^{3} c d^{9} - 533 \, a^{8} b^{2} d^{10}\right )} x^{2} + 6 \, {\left (4 \, b^{10} c^{9} d + 9 \, a b^{9} c^{8} d^{2} + 24 \, a^{2} b^{8} c^{7} d^{3} + 84 \, a^{3} b^{7} c^{6} d^{4} + 504 \, a^{4} b^{6} c^{5} d^{5} - 5754 \, a^{5} b^{5} c^{4} d^{6} + 14616 \, a^{6} b^{4} c^{3} d^{7} - 16524 \, a^{7} b^{3} c^{2} d^{8} + 8916 \, a^{8} b^{2} c d^{9} - 1879 \, a^{9} b d^{10}\right )} x}{12 \, {\left (b^{17} x^{6} + 6 \, a b^{16} x^{5} + 15 \, a^{2} b^{15} x^{4} + 20 \, a^{3} b^{14} x^{3} + 15 \, a^{4} b^{13} x^{2} + 6 \, a^{5} b^{12} x + a^{6} b^{11}\right )}} + \frac {3 \, b^{3} d^{10} x^{4} + 4 \, {\left (10 \, b^{3} c d^{9} - 7 \, a b^{2} d^{10}\right )} x^{3} + 6 \, {\left (45 \, b^{3} c^{2} d^{8} - 70 \, a b^{2} c d^{9} + 28 \, a^{2} b d^{10}\right )} x^{2} + 12 \, {\left (120 \, b^{3} c^{3} d^{7} - 315 \, a b^{2} c^{2} d^{8} + 280 \, a^{2} b c d^{9} - 84 \, a^{3} d^{10}\right )} x}{12 \, b^{10}} + \frac {210 \, {\left (b^{4} c^{4} d^{6} - 4 \, a b^{3} c^{3} d^{7} + 6 \, a^{2} b^{2} c^{2} d^{8} - 4 \, a^{3} b c d^{9} + a^{4} 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. 1386 vs.
\(2 (252) = 504\).
time = 1.10, size = 1386, normalized size = 5.29 \begin {gather*} \frac {3 \, b^{10} d^{10} x^{10} - 2 \, b^{10} c^{10} - 4 \, a b^{9} c^{9} d - 9 \, a^{2} b^{8} c^{8} d^{2} - 24 \, a^{3} b^{7} c^{7} d^{3} - 84 \, a^{4} b^{6} c^{6} d^{4} - 504 \, a^{5} b^{5} c^{5} d^{5} + 6174 \, a^{6} b^{4} c^{4} d^{6} - 16056 \, a^{7} b^{3} c^{3} d^{7} + 18414 \, a^{8} b^{2} c^{2} d^{8} - 10036 \, a^{9} b c d^{9} + 2131 \, a^{10} d^{10} + 10 \, {\left (4 \, b^{10} c d^{9} - a b^{9} d^{10}\right )} x^{9} + 45 \, {\left (6 \, b^{10} c^{2} d^{8} - 4 \, a b^{9} c d^{9} + a^{2} b^{8} d^{10}\right )} x^{8} + 360 \, {\left (4 \, b^{10} c^{3} d^{7} - 6 \, a b^{9} c^{2} d^{8} + 4 \, a^{2} b^{8} c d^{9} - a^{3} b^{7} d^{10}\right )} x^{7} + {\left (8640 \, a b^{9} c^{3} d^{7} - 18630 \, a^{2} b^{8} c^{2} d^{8} + 14660 \, a^{3} b^{7} c d^{9} - 4043 \, a^{4} b^{6} d^{10}\right )} x^{6} - 6 \, {\left (504 \, b^{10} c^{5} d^{5} - 2520 \, a b^{9} c^{4} d^{6} + 1440 \, a^{2} b^{8} c^{3} d^{7} + 3510 \, a^{3} b^{7} c^{2} d^{8} - 4580 \, a^{4} b^{6} c d^{9} + 1523 \, a^{5} b^{5} d^{10}\right )} x^{5} - 15 \, {\left (84 \, b^{10} c^{6} d^{4} + 504 \, a b^{9} c^{5} d^{5} - 3780 \, a^{2} b^{8} c^{4} d^{6} + 6480 \, a^{3} b^{7} c^{3} d^{7} - 4050 \, a^{4} b^{6} c^{2} d^{8} + 460 \, a^{5} b^{5} c d^{9} + 263 \, a^{6} b^{4} d^{10}\right )} x^{4} - 20 \, {\left (24 \, b^{10} c^{7} d^{3} + 84 \, a b^{9} c^{6} d^{4} + 504 \, a^{2} b^{8} c^{5} d^{5} - 4620 \, a^{3} b^{7} c^{4} d^{6} + 9840 \, a^{4} b^{6} c^{3} d^{7} - 9090 \, a^{5} b^{5} c^{2} d^{8} + 3820 \, a^{6} b^{4} c d^{9} - 577 \, a^{7} b^{3} d^{10}\right )} x^{3} - 15 \, {\left (9 \, b^{10} c^{8} d^{2} + 24 \, a b^{9} c^{7} d^{3} + 84 \, a^{2} b^{8} c^{6} d^{4} + 504 \, a^{3} b^{7} c^{5} d^{5} - 5250 \, a^{4} b^{6} c^{4} d^{6} + 12360 \, a^{5} b^{5} c^{3} d^{7} - 12870 \, a^{6} b^{4} c^{2} d^{8} + 6340 \, a^{7} b^{3} c d^{9} - 1207 \, a^{8} b^{2} d^{10}\right )} x^{2} - 6 \, {\left (4 \, b^{10} c^{9} d + 9 \, a b^{9} c^{8} d^{2} + 24 \, a^{2} b^{8} c^{7} d^{3} + 84 \, a^{3} b^{7} c^{6} d^{4} + 504 \, a^{4} b^{6} c^{5} d^{5} - 5754 \, a^{5} b^{5} c^{4} d^{6} + 14376 \, a^{6} b^{4} c^{3} d^{7} - 15894 \, a^{7} b^{3} c^{2} d^{8} + 8356 \, a^{8} b^{2} c d^{9} - 1711 \, a^{9} b d^{10}\right )} x + 2520 \, {\left (a^{6} b^{4} c^{4} d^{6} - 4 \, a^{7} b^{3} c^{3} d^{7} + 6 \, a^{8} b^{2} c^{2} d^{8} - 4 \, a^{9} b c d^{9} + a^{10} d^{10} + {\left (b^{10} c^{4} d^{6} - 4 \, a b^{9} c^{3} d^{7} + 6 \, a^{2} b^{8} c^{2} d^{8} - 4 \, a^{3} b^{7} c d^{9} + a^{4} b^{6} d^{10}\right )} x^{6} + 6 \, {\left (a b^{9} c^{4} d^{6} - 4 \, a^{2} b^{8} c^{3} d^{7} + 6 \, a^{3} b^{7} c^{2} d^{8} - 4 \, a^{4} b^{6} c d^{9} + a^{5} b^{5} d^{10}\right )} x^{5} + 15 \, {\left (a^{2} b^{8} c^{4} d^{6} - 4 \, a^{3} b^{7} c^{3} d^{7} + 6 \, a^{4} b^{6} c^{2} d^{8} - 4 \, a^{5} b^{5} c d^{9} + a^{6} b^{4} d^{10}\right )} x^{4} + 20 \, {\left (a^{3} b^{7} c^{4} d^{6} - 4 \, a^{4} b^{6} c^{3} d^{7} + 6 \, a^{5} b^{5} c^{2} d^{8} - 4 \, a^{6} b^{4} c d^{9} + a^{7} b^{3} d^{10}\right )} x^{3} + 15 \, {\left (a^{4} b^{6} c^{4} d^{6} - 4 \, a^{5} b^{5} c^{3} d^{7} + 6 \, a^{6} b^{4} c^{2} d^{8} - 4 \, a^{7} b^{3} c d^{9} + a^{8} b^{2} d^{10}\right )} x^{2} + 6 \, {\left (a^{5} b^{5} c^{4} d^{6} - 4 \, a^{6} b^{4} c^{3} d^{7} + 6 \, a^{7} b^{3} c^{2} d^{8} - 4 \, a^{8} b^{2} c d^{9} + a^{9} b d^{10}\right )} x\right )} \log \left (b x + a\right )}{12 \, {\left (b^{17} x^{6} + 6 \, a b^{16} x^{5} + 15 \, a^{2} b^{15} x^{4} + 20 \, a^{3} b^{14} x^{3} + 15 \, a^{4} b^{13} x^{2} + 6 \, a^{5} b^{12} x + a^{6} b^{11}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \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. 878 vs.
\(2 (252) = 504\).
time = 0.54, size = 878, normalized size = 3.35 \begin {gather*} \frac {210 \, {\left (b^{4} c^{4} d^{6} - 4 \, a b^{3} c^{3} d^{7} + 6 \, a^{2} b^{2} c^{2} d^{8} - 4 \, a^{3} b c d^{9} + a^{4} d^{10}\right )} \log \left ({\left | b x + a \right |}\right )}{b^{11}} - \frac {2 \, b^{10} c^{10} + 4 \, a b^{9} c^{9} d + 9 \, a^{2} b^{8} c^{8} d^{2} + 24 \, a^{3} b^{7} c^{7} d^{3} + 84 \, a^{4} b^{6} c^{6} d^{4} + 504 \, a^{5} b^{5} c^{5} d^{5} - 6174 \, a^{6} b^{4} c^{4} d^{6} + 16056 \, a^{7} b^{3} c^{3} d^{7} - 18414 \, a^{8} b^{2} c^{2} d^{8} + 10036 \, a^{9} b c d^{9} - 2131 \, a^{10} d^{10} + 3024 \, {\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 )} x^{5} + 1260 \, {\left (b^{10} c^{6} d^{4} + 6 \, a b^{9} c^{5} d^{5} - 45 \, a^{2} b^{8} c^{4} d^{6} + 100 \, a^{3} b^{7} c^{3} d^{7} - 105 \, a^{4} b^{6} c^{2} d^{8} + 54 \, a^{5} b^{5} c d^{9} - 11 \, a^{6} b^{4} d^{10}\right )} x^{4} + 240 \, {\left (2 \, b^{10} c^{7} d^{3} + 7 \, a b^{9} c^{6} d^{4} + 42 \, a^{2} b^{8} c^{5} d^{5} - 385 \, a^{3} b^{7} c^{4} d^{6} + 910 \, a^{4} b^{6} c^{3} d^{7} - 987 \, a^{5} b^{5} c^{2} d^{8} + 518 \, a^{6} b^{4} c d^{9} - 107 \, a^{7} b^{3} d^{10}\right )} x^{3} + 45 \, {\left (3 \, b^{10} c^{8} d^{2} + 8 \, a b^{9} c^{7} d^{3} + 28 \, a^{2} b^{8} c^{6} d^{4} + 168 \, a^{3} b^{7} c^{5} d^{5} - 1750 \, a^{4} b^{6} c^{4} d^{6} + 4312 \, a^{5} b^{5} c^{3} d^{7} - 4788 \, a^{6} b^{4} c^{2} d^{8} + 2552 \, a^{7} b^{3} c d^{9} - 533 \, a^{8} b^{2} d^{10}\right )} x^{2} + 6 \, {\left (4 \, b^{10} c^{9} d + 9 \, a b^{9} c^{8} d^{2} + 24 \, a^{2} b^{8} c^{7} d^{3} + 84 \, a^{3} b^{7} c^{6} d^{4} + 504 \, a^{4} b^{6} c^{5} d^{5} - 5754 \, a^{5} b^{5} c^{4} d^{6} + 14616 \, a^{6} b^{4} c^{3} d^{7} - 16524 \, a^{7} b^{3} c^{2} d^{8} + 8916 \, a^{8} b^{2} c d^{9} - 1879 \, a^{9} b d^{10}\right )} x}{12 \, {\left (b x + a\right )}^{6} b^{11}} + \frac {3 \, b^{21} d^{10} x^{4} + 40 \, b^{21} c d^{9} x^{3} - 28 \, a b^{20} d^{10} x^{3} + 270 \, b^{21} c^{2} d^{8} x^{2} - 420 \, a b^{20} c d^{9} x^{2} + 168 \, a^{2} b^{19} d^{10} x^{2} + 1440 \, b^{21} c^{3} d^{7} x - 3780 \, a b^{20} c^{2} d^{8} x + 3360 \, a^{2} b^{19} c d^{9} x - 1008 \, a^{3} b^{18} d^{10} x}{12 \, b^{28}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.42, size = 997, normalized size = 3.81 \begin {gather*} x^2\,\left (\frac {7\,a\,\left (\frac {7\,a\,d^{10}}{b^8}-\frac {10\,c\,d^9}{b^7}\right )}{2\,b}-\frac {21\,a^2\,d^{10}}{2\,b^9}+\frac {45\,c^2\,d^8}{2\,b^7}\right )-\frac {x^4\,\left (-1155\,a^6\,b^3\,d^{10}+5670\,a^5\,b^4\,c\,d^9-11025\,a^4\,b^5\,c^2\,d^8+10500\,a^3\,b^6\,c^3\,d^7-4725\,a^2\,b^7\,c^4\,d^6+630\,a\,b^8\,c^5\,d^5+105\,b^9\,c^6\,d^4\right )+\frac {-2131\,a^{10}\,d^{10}+10036\,a^9\,b\,c\,d^9-18414\,a^8\,b^2\,c^2\,d^8+16056\,a^7\,b^3\,c^3\,d^7-6174\,a^6\,b^4\,c^4\,d^6+504\,a^5\,b^5\,c^5\,d^5+84\,a^4\,b^6\,c^6\,d^4+24\,a^3\,b^7\,c^7\,d^3+9\,a^2\,b^8\,c^8\,d^2+4\,a\,b^9\,c^9\,d+2\,b^{10}\,c^{10}}{12\,b}+x\,\left (-\frac {1879\,a^9\,d^{10}}{2}+4458\,a^8\,b\,c\,d^9-8262\,a^7\,b^2\,c^2\,d^8+7308\,a^6\,b^3\,c^3\,d^7-2877\,a^5\,b^4\,c^4\,d^6+252\,a^4\,b^5\,c^5\,d^5+42\,a^3\,b^6\,c^6\,d^4+12\,a^2\,b^7\,c^7\,d^3+\frac {9\,a\,b^8\,c^8\,d^2}{2}+2\,b^9\,c^9\,d\right )+x^3\,\left (-2140\,a^7\,b^2\,d^{10}+10360\,a^6\,b^3\,c\,d^9-19740\,a^5\,b^4\,c^2\,d^8+18200\,a^4\,b^5\,c^3\,d^7-7700\,a^3\,b^6\,c^4\,d^6+840\,a^2\,b^7\,c^5\,d^5+140\,a\,b^8\,c^6\,d^4+40\,b^9\,c^7\,d^3\right )+x^2\,\left (-\frac {7995\,a^8\,b\,d^{10}}{4}+9570\,a^7\,b^2\,c\,d^9-17955\,a^6\,b^3\,c^2\,d^8+16170\,a^5\,b^4\,c^3\,d^7-\frac {13125\,a^4\,b^5\,c^4\,d^6}{2}+630\,a^3\,b^6\,c^5\,d^5+105\,a^2\,b^7\,c^6\,d^4+30\,a\,b^8\,c^7\,d^3+\frac {45\,b^9\,c^8\,d^2}{4}\right )-x^5\,\left (252\,a^5\,b^4\,d^{10}-1260\,a^4\,b^5\,c\,d^9+2520\,a^3\,b^6\,c^2\,d^8-2520\,a^2\,b^7\,c^3\,d^7+1260\,a\,b^8\,c^4\,d^6-252\,b^9\,c^5\,d^5\right )}{a^6\,b^{10}+6\,a^5\,b^{11}\,x+15\,a^4\,b^{12}\,x^2+20\,a^3\,b^{13}\,x^3+15\,a^2\,b^{14}\,x^4+6\,a\,b^{15}\,x^5+b^{16}\,x^6}-x^3\,\left (\frac {7\,a\,d^{10}}{3\,b^8}-\frac {10\,c\,d^9}{3\,b^7}\right )-x\,\left (\frac {7\,a\,\left (\frac {7\,a\,\left (\frac {7\,a\,d^{10}}{b^8}-\frac {10\,c\,d^9}{b^7}\right )}{b}-\frac {21\,a^2\,d^{10}}{b^9}+\frac {45\,c^2\,d^8}{b^7}\right )}{b}+\frac {35\,a^3\,d^{10}}{b^{10}}-\frac {120\,c^3\,d^7}{b^7}-\frac {21\,a^2\,\left (\frac {7\,a\,d^{10}}{b^8}-\frac {10\,c\,d^9}{b^7}\right )}{b^2}\right )+\frac {\ln \left (a+b\,x\right )\,\left (210\,a^4\,d^{10}-840\,a^3\,b\,c\,d^9+1260\,a^2\,b^2\,c^2\,d^8-840\,a\,b^3\,c^3\,d^7+210\,b^4\,c^4\,d^6\right )}{b^{11}}+\frac {d^{10}\,x^4}{4\,b^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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