Optimal. Leaf size=47 \[ \frac{a^2 (a+b x)^8}{8 b^3}+\frac{(a+b x)^{10}}{10 b^3}-\frac{2 a (a+b x)^9}{9 b^3} \]
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Rubi [A] time = 0.0236088, antiderivative size = 47, 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} \[ \frac{a^2 (a+b x)^8}{8 b^3}+\frac{(a+b x)^{10}}{10 b^3}-\frac{2 a (a+b x)^9}{9 b^3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^2 (a+b x)^7 \, dx &=\int \left (\frac{a^2 (a+b x)^7}{b^2}-\frac{2 a (a+b x)^8}{b^2}+\frac{(a+b x)^9}{b^2}\right ) \, dx\\ &=\frac{a^2 (a+b x)^8}{8 b^3}-\frac{2 a (a+b x)^9}{9 b^3}+\frac{(a+b x)^{10}}{10 b^3}\\ \end{align*}
Mathematica [A] time = 0.0026457, size = 93, normalized size = 1.98 \[ \frac{21}{8} a^2 b^5 x^8+5 a^3 b^4 x^7+\frac{35}{6} a^4 b^3 x^6+\frac{21}{5} a^5 b^2 x^5+\frac{7}{4} a^6 b x^4+\frac{a^7 x^3}{3}+\frac{7}{9} a b^6 x^9+\frac{b^7 x^{10}}{10} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 80, normalized size = 1.7 \begin{align*}{\frac{{b}^{7}{x}^{10}}{10}}+{\frac{7\,a{b}^{6}{x}^{9}}{9}}+{\frac{21\,{a}^{2}{b}^{5}{x}^{8}}{8}}+5\,{a}^{3}{b}^{4}{x}^{7}+{\frac{35\,{a}^{4}{b}^{3}{x}^{6}}{6}}+{\frac{21\,{a}^{5}{b}^{2}{x}^{5}}{5}}+{\frac{7\,{a}^{6}b{x}^{4}}{4}}+{\frac{{a}^{7}{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04321, size = 107, normalized size = 2.28 \begin{align*} \frac{1}{10} \, b^{7} x^{10} + \frac{7}{9} \, a b^{6} x^{9} + \frac{21}{8} \, a^{2} b^{5} x^{8} + 5 \, a^{3} b^{4} x^{7} + \frac{35}{6} \, a^{4} b^{3} x^{6} + \frac{21}{5} \, a^{5} b^{2} x^{5} + \frac{7}{4} \, a^{6} b x^{4} + \frac{1}{3} \, a^{7} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40097, size = 181, normalized size = 3.85 \begin{align*} \frac{1}{10} x^{10} b^{7} + \frac{7}{9} x^{9} b^{6} a + \frac{21}{8} x^{8} b^{5} a^{2} + 5 x^{7} b^{4} a^{3} + \frac{35}{6} x^{6} b^{3} a^{4} + \frac{21}{5} x^{5} b^{2} a^{5} + \frac{7}{4} x^{4} b a^{6} + \frac{1}{3} x^{3} a^{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.089851, size = 92, normalized size = 1.96 \begin{align*} \frac{a^{7} x^{3}}{3} + \frac{7 a^{6} b x^{4}}{4} + \frac{21 a^{5} b^{2} x^{5}}{5} + \frac{35 a^{4} b^{3} x^{6}}{6} + 5 a^{3} b^{4} x^{7} + \frac{21 a^{2} b^{5} x^{8}}{8} + \frac{7 a b^{6} x^{9}}{9} + \frac{b^{7} x^{10}}{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18946, size = 107, normalized size = 2.28 \begin{align*} \frac{1}{10} \, b^{7} x^{10} + \frac{7}{9} \, a b^{6} x^{9} + \frac{21}{8} \, a^{2} b^{5} x^{8} + 5 \, a^{3} b^{4} x^{7} + \frac{35}{6} \, a^{4} b^{3} x^{6} + \frac{21}{5} \, a^{5} b^{2} x^{5} + \frac{7}{4} \, a^{6} b x^{4} + \frac{1}{3} \, a^{7} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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