Optimal. Leaf size=47 \[ \frac{b^2 (a x+b)^9}{9 a^3}+\frac{(a x+b)^{11}}{11 a^3}-\frac{b (a x+b)^{10}}{5 a^3} \]
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Rubi [A] time = 0.0282751, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {263, 43} \[ \frac{b^2 (a x+b)^9}{9 a^3}+\frac{(a x+b)^{11}}{11 a^3}-\frac{b (a x+b)^{10}}{5 a^3} \]
Antiderivative was successfully verified.
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Rule 263
Rule 43
Rubi steps
\begin{align*} \int \left (a+\frac{b}{x}\right )^8 x^{10} \, dx &=\int x^2 (b+a x)^8 \, dx\\ &=\int \left (\frac{b^2 (b+a x)^8}{a^2}-\frac{2 b (b+a x)^9}{a^2}+\frac{(b+a x)^{10}}{a^2}\right ) \, dx\\ &=\frac{b^2 (b+a x)^9}{9 a^3}-\frac{b (b+a x)^{10}}{5 a^3}+\frac{(b+a x)^{11}}{11 a^3}\\ \end{align*}
Mathematica [B] time = 0.0024365, size = 102, normalized size = 2.17 \[ \frac{28}{9} a^6 b^2 x^9+7 a^5 b^3 x^8+10 a^4 b^4 x^7+\frac{28}{3} a^3 b^5 x^6+\frac{28}{5} a^2 b^6 x^5+\frac{4}{5} a^7 b x^{10}+\frac{a^8 x^{11}}{11}+2 a b^7 x^4+\frac{b^8 x^3}{3} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.001, size = 91, normalized size = 1.9 \begin{align*}{\frac{{a}^{8}{x}^{11}}{11}}+{\frac{4\,{a}^{7}b{x}^{10}}{5}}+{\frac{28\,{b}^{2}{a}^{6}{x}^{9}}{9}}+7\,{a}^{5}{b}^{3}{x}^{8}+10\,{a}^{4}{b}^{4}{x}^{7}+{\frac{28\,{a}^{3}{b}^{5}{x}^{6}}{3}}+{\frac{28\,{b}^{6}{a}^{2}{x}^{5}}{5}}+2\,{b}^{7}a{x}^{4}+{\frac{{b}^{8}{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.970426, size = 122, normalized size = 2.6 \begin{align*} \frac{1}{11} \, a^{8} x^{11} + \frac{4}{5} \, a^{7} b x^{10} + \frac{28}{9} \, a^{6} b^{2} x^{9} + 7 \, a^{5} b^{3} x^{8} + 10 \, a^{4} b^{4} x^{7} + \frac{28}{3} \, a^{3} b^{5} x^{6} + \frac{28}{5} \, a^{2} b^{6} x^{5} + 2 \, a b^{7} x^{4} + \frac{1}{3} \, b^{8} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.40237, size = 203, normalized size = 4.32 \begin{align*} \frac{1}{11} \, a^{8} x^{11} + \frac{4}{5} \, a^{7} b x^{10} + \frac{28}{9} \, a^{6} b^{2} x^{9} + 7 \, a^{5} b^{3} x^{8} + 10 \, a^{4} b^{4} x^{7} + \frac{28}{3} \, a^{3} b^{5} x^{6} + \frac{28}{5} \, a^{2} b^{6} x^{5} + 2 \, a b^{7} x^{4} + \frac{1}{3} \, b^{8} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.078168, size = 102, normalized size = 2.17 \begin{align*} \frac{a^{8} x^{11}}{11} + \frac{4 a^{7} b x^{10}}{5} + \frac{28 a^{6} b^{2} x^{9}}{9} + 7 a^{5} b^{3} x^{8} + 10 a^{4} b^{4} x^{7} + \frac{28 a^{3} b^{5} x^{6}}{3} + \frac{28 a^{2} b^{6} x^{5}}{5} + 2 a b^{7} x^{4} + \frac{b^{8} x^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.19003, size = 122, normalized size = 2.6 \begin{align*} \frac{1}{11} \, a^{8} x^{11} + \frac{4}{5} \, a^{7} b x^{10} + \frac{28}{9} \, a^{6} b^{2} x^{9} + 7 \, a^{5} b^{3} x^{8} + 10 \, a^{4} b^{4} x^{7} + \frac{28}{3} \, a^{3} b^{5} x^{6} + \frac{28}{5} \, a^{2} b^{6} x^{5} + 2 \, a b^{7} x^{4} + \frac{1}{3} \, b^{8} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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