Optimal. Leaf size=64 \[ \frac{a^2 (a+b x)^9}{3 b^4}-\frac{a^3 (a+b x)^8}{8 b^4}+\frac{(a+b x)^{11}}{11 b^4}-\frac{3 a (a+b x)^{10}}{10 b^4} \]
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Rubi [A] time = 0.0299538, 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} \[ \frac{a^2 (a+b x)^9}{3 b^4}-\frac{a^3 (a+b x)^8}{8 b^4}+\frac{(a+b x)^{11}}{11 b^4}-\frac{3 a (a+b x)^{10}}{10 b^4} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^3 (a+b x)^7 \, dx &=\int \left (-\frac{a^3 (a+b x)^7}{b^3}+\frac{3 a^2 (a+b x)^8}{b^3}-\frac{3 a (a+b x)^9}{b^3}+\frac{(a+b x)^{10}}{b^3}\right ) \, dx\\ &=-\frac{a^3 (a+b x)^8}{8 b^4}+\frac{a^2 (a+b x)^9}{3 b^4}-\frac{3 a (a+b x)^{10}}{10 b^4}+\frac{(a+b x)^{11}}{11 b^4}\\ \end{align*}
Mathematica [A] time = 0.0025907, size = 93, normalized size = 1.45 \[ \frac{7}{3} a^2 b^5 x^9+\frac{35}{8} a^3 b^4 x^8+5 a^4 b^3 x^7+\frac{7}{2} a^5 b^2 x^6+\frac{7}{5} a^6 b x^5+\frac{a^7 x^4}{4}+\frac{7}{10} a b^6 x^{10}+\frac{b^7 x^{11}}{11} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 80, normalized size = 1.3 \begin{align*}{\frac{{b}^{7}{x}^{11}}{11}}+{\frac{7\,a{b}^{6}{x}^{10}}{10}}+{\frac{7\,{a}^{2}{b}^{5}{x}^{9}}{3}}+{\frac{35\,{a}^{3}{b}^{4}{x}^{8}}{8}}+5\,{a}^{4}{b}^{3}{x}^{7}+{\frac{7\,{a}^{5}{b}^{2}{x}^{6}}{2}}+{\frac{7\,{a}^{6}b{x}^{5}}{5}}+{\frac{{a}^{7}{x}^{4}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01883, size = 107, normalized size = 1.67 \begin{align*} \frac{1}{11} \, b^{7} x^{11} + \frac{7}{10} \, a b^{6} x^{10} + \frac{7}{3} \, a^{2} b^{5} x^{9} + \frac{35}{8} \, a^{3} b^{4} x^{8} + 5 \, a^{4} b^{3} x^{7} + \frac{7}{2} \, a^{5} b^{2} x^{6} + \frac{7}{5} \, a^{6} b x^{5} + \frac{1}{4} \, a^{7} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49904, size = 181, normalized size = 2.83 \begin{align*} \frac{1}{11} x^{11} b^{7} + \frac{7}{10} x^{10} b^{6} a + \frac{7}{3} x^{9} b^{5} a^{2} + \frac{35}{8} x^{8} b^{4} a^{3} + 5 x^{7} b^{3} a^{4} + \frac{7}{2} x^{6} b^{2} a^{5} + \frac{7}{5} x^{5} b a^{6} + \frac{1}{4} x^{4} a^{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.087945, size = 92, normalized size = 1.44 \begin{align*} \frac{a^{7} x^{4}}{4} + \frac{7 a^{6} b x^{5}}{5} + \frac{7 a^{5} b^{2} x^{6}}{2} + 5 a^{4} b^{3} x^{7} + \frac{35 a^{3} b^{4} x^{8}}{8} + \frac{7 a^{2} b^{5} x^{9}}{3} + \frac{7 a b^{6} x^{10}}{10} + \frac{b^{7} x^{11}}{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16786, size = 107, normalized size = 1.67 \begin{align*} \frac{1}{11} \, b^{7} x^{11} + \frac{7}{10} \, a b^{6} x^{10} + \frac{7}{3} \, a^{2} b^{5} x^{9} + \frac{35}{8} \, a^{3} b^{4} x^{8} + 5 \, a^{4} b^{3} x^{7} + \frac{7}{2} \, a^{5} b^{2} x^{6} + \frac{7}{5} \, a^{6} b x^{5} + \frac{1}{4} \, a^{7} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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