Optimal. Leaf size=30 \[ \frac{(a+b x)^9}{9 b^2}-\frac{a (a+b x)^8}{8 b^2} \]
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Rubi [A] time = 0.0081933, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {43} \[ \frac{(a+b x)^9}{9 b^2}-\frac{a (a+b x)^8}{8 b^2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x (a+b x)^7 \, dx &=\int \left (-\frac{a (a+b x)^7}{b}+\frac{(a+b x)^8}{b}\right ) \, dx\\ &=-\frac{a (a+b x)^8}{8 b^2}+\frac{(a+b x)^9}{9 b^2}\\ \end{align*}
Mathematica [B] time = 0.0025274, size = 91, normalized size = 3.03 \[ 3 a^2 b^5 x^7+\frac{35}{6} a^3 b^4 x^6+7 a^4 b^3 x^5+\frac{21}{4} a^5 b^2 x^4+\frac{7}{3} a^6 b x^3+\frac{a^7 x^2}{2}+\frac{7}{8} a b^6 x^8+\frac{b^7 x^9}{9} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.002, size = 80, normalized size = 2.7 \begin{align*}{\frac{{b}^{7}{x}^{9}}{9}}+{\frac{7\,a{b}^{6}{x}^{8}}{8}}+3\,{a}^{2}{b}^{5}{x}^{7}+{\frac{35\,{a}^{3}{b}^{4}{x}^{6}}{6}}+7\,{a}^{4}{b}^{3}{x}^{5}+{\frac{21\,{a}^{5}{b}^{2}{x}^{4}}{4}}+{\frac{7\,{a}^{6}b{x}^{3}}{3}}+{\frac{{a}^{7}{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.01952, size = 107, normalized size = 3.57 \begin{align*} \frac{1}{9} \, b^{7} x^{9} + \frac{7}{8} \, a b^{6} x^{8} + 3 \, a^{2} b^{5} x^{7} + \frac{35}{6} \, a^{3} b^{4} x^{6} + 7 \, a^{4} b^{3} x^{5} + \frac{21}{4} \, a^{5} b^{2} x^{4} + \frac{7}{3} \, a^{6} b x^{3} + \frac{1}{2} \, a^{7} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.38148, size = 174, normalized size = 5.8 \begin{align*} \frac{1}{9} x^{9} b^{7} + \frac{7}{8} x^{8} b^{6} a + 3 x^{7} b^{5} a^{2} + \frac{35}{6} x^{6} b^{4} a^{3} + 7 x^{5} b^{3} a^{4} + \frac{21}{4} x^{4} b^{2} a^{5} + \frac{7}{3} x^{3} b a^{6} + \frac{1}{2} x^{2} a^{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.0818, size = 90, normalized size = 3. \begin{align*} \frac{a^{7} x^{2}}{2} + \frac{7 a^{6} b x^{3}}{3} + \frac{21 a^{5} b^{2} x^{4}}{4} + 7 a^{4} b^{3} x^{5} + \frac{35 a^{3} b^{4} x^{6}}{6} + 3 a^{2} b^{5} x^{7} + \frac{7 a b^{6} x^{8}}{8} + \frac{b^{7} x^{9}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.21016, size = 107, normalized size = 3.57 \begin{align*} \frac{1}{9} \, b^{7} x^{9} + \frac{7}{8} \, a b^{6} x^{8} + 3 \, a^{2} b^{5} x^{7} + \frac{35}{6} \, a^{3} b^{4} x^{6} + 7 \, a^{4} b^{3} x^{5} + \frac{21}{4} \, a^{5} b^{2} x^{4} + \frac{7}{3} \, a^{6} b x^{3} + \frac{1}{2} \, a^{7} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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