Optimal. Leaf size=64 \[ \frac{a^3}{9 b^4 (a+b x)^9}-\frac{3 a^2}{8 b^4 (a+b x)^8}+\frac{3 a}{7 b^4 (a+b x)^7}-\frac{1}{6 b^4 (a+b x)^6} \]
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Rubi [A] time = 0.0297847, antiderivative size = 64, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ \frac{a^3}{9 b^4 (a+b x)^9}-\frac{3 a^2}{8 b^4 (a+b x)^8}+\frac{3 a}{7 b^4 (a+b x)^7}-\frac{1}{6 b^4 (a+b x)^6} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{x^3}{(a+b x)^{10}} \, dx &=\int \left (-\frac{a^3}{b^3 (a+b x)^{10}}+\frac{3 a^2}{b^3 (a+b x)^9}-\frac{3 a}{b^3 (a+b x)^8}+\frac{1}{b^3 (a+b x)^7}\right ) \, dx\\ &=\frac{a^3}{9 b^4 (a+b x)^9}-\frac{3 a^2}{8 b^4 (a+b x)^8}+\frac{3 a}{7 b^4 (a+b x)^7}-\frac{1}{6 b^4 (a+b x)^6}\\ \end{align*}
Mathematica [A] time = 0.0178355, size = 42, normalized size = 0.66 \[ -\frac{9 a^2 b x+a^3+36 a b^2 x^2+84 b^3 x^3}{504 b^4 (a+b x)^9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 57, normalized size = 0.9 \begin{align*}{\frac{{a}^{3}}{9\,{b}^{4} \left ( bx+a \right ) ^{9}}}-{\frac{3\,{a}^{2}}{8\,{b}^{4} \left ( bx+a \right ) ^{8}}}+{\frac{3\,a}{7\,{b}^{4} \left ( bx+a \right ) ^{7}}}-{\frac{1}{6\,{b}^{4} \left ( bx+a \right ) ^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.09933, size = 177, normalized size = 2.77 \begin{align*} -\frac{84 \, b^{3} x^{3} + 36 \, a b^{2} x^{2} + 9 \, a^{2} b x + a^{3}}{504 \,{\left (b^{13} x^{9} + 9 \, a b^{12} x^{8} + 36 \, a^{2} b^{11} x^{7} + 84 \, a^{3} b^{10} x^{6} + 126 \, a^{4} b^{9} x^{5} + 126 \, a^{5} b^{8} x^{4} + 84 \, a^{6} b^{7} x^{3} + 36 \, a^{7} b^{6} x^{2} + 9 \, a^{8} b^{5} x + a^{9} b^{4}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.47435, size = 284, normalized size = 4.44 \begin{align*} -\frac{84 \, b^{3} x^{3} + 36 \, a b^{2} x^{2} + 9 \, a^{2} b x + a^{3}}{504 \,{\left (b^{13} x^{9} + 9 \, a b^{12} x^{8} + 36 \, a^{2} b^{11} x^{7} + 84 \, a^{3} b^{10} x^{6} + 126 \, a^{4} b^{9} x^{5} + 126 \, a^{5} b^{8} x^{4} + 84 \, a^{6} b^{7} x^{3} + 36 \, a^{7} b^{6} x^{2} + 9 \, a^{8} b^{5} x + a^{9} b^{4}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.10376, size = 139, normalized size = 2.17 \begin{align*} - \frac{a^{3} + 9 a^{2} b x + 36 a b^{2} x^{2} + 84 b^{3} x^{3}}{504 a^{9} b^{4} + 4536 a^{8} b^{5} x + 18144 a^{7} b^{6} x^{2} + 42336 a^{6} b^{7} x^{3} + 63504 a^{5} b^{8} x^{4} + 63504 a^{4} b^{9} x^{5} + 42336 a^{3} b^{10} x^{6} + 18144 a^{2} b^{11} x^{7} + 4536 a b^{12} x^{8} + 504 b^{13} x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21656, size = 54, normalized size = 0.84 \begin{align*} -\frac{84 \, b^{3} x^{3} + 36 \, a b^{2} x^{2} + 9 \, a^{2} b x + a^{3}}{504 \,{\left (b x + a\right )}^{9} b^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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