Optimal. Leaf size=30 \[ \frac{(a+b x)^7}{7 b^2}-\frac{a (a+b x)^6}{6 b^2} \]
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Rubi [A] time = 0.0079793, 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} \[ \frac{(a+b x)^7}{7 b^2}-\frac{a (a+b x)^6}{6 b^2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x (a+b x)^5 \, dx &=\int \left (-\frac{a (a+b x)^5}{b}+\frac{(a+b x)^6}{b}\right ) \, dx\\ &=-\frac{a (a+b x)^6}{6 b^2}+\frac{(a+b x)^7}{7 b^2}\\ \end{align*}
Mathematica [B] time = 0.0020969, size = 67, normalized size = 2.23 \[ 2 a^2 b^3 x^5+\frac{5}{2} a^3 b^2 x^4+\frac{5}{3} a^4 b x^3+\frac{a^5 x^2}{2}+\frac{5}{6} a b^4 x^6+\frac{b^5 x^7}{7} \]
Antiderivative was successfully verified.
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Maple [B] time = 0., size = 58, normalized size = 1.9 \begin{align*}{\frac{{b}^{5}{x}^{7}}{7}}+{\frac{5\,a{b}^{4}{x}^{6}}{6}}+2\,{a}^{2}{b}^{3}{x}^{5}+{\frac{5\,{a}^{3}{b}^{2}{x}^{4}}{2}}+{\frac{5\,{a}^{4}b{x}^{3}}{3}}+{\frac{{a}^{5}{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.03267, size = 77, normalized size = 2.57 \begin{align*} \frac{1}{7} \, b^{5} x^{7} + \frac{5}{6} \, a b^{4} x^{6} + 2 \, a^{2} b^{3} x^{5} + \frac{5}{2} \, a^{3} b^{2} x^{4} + \frac{5}{3} \, a^{4} b x^{3} + \frac{1}{2} \, a^{5} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.35533, size = 126, normalized size = 4.2 \begin{align*} \frac{1}{7} x^{7} b^{5} + \frac{5}{6} x^{6} b^{4} a + 2 x^{5} b^{3} a^{2} + \frac{5}{2} x^{4} b^{2} a^{3} + \frac{5}{3} x^{3} b a^{4} + \frac{1}{2} x^{2} a^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.076103, size = 65, normalized size = 2.17 \begin{align*} \frac{a^{5} x^{2}}{2} + \frac{5 a^{4} b x^{3}}{3} + \frac{5 a^{3} b^{2} x^{4}}{2} + 2 a^{2} b^{3} x^{5} + \frac{5 a b^{4} x^{6}}{6} + \frac{b^{5} x^{7}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.16592, size = 77, normalized size = 2.57 \begin{align*} \frac{1}{7} \, b^{5} x^{7} + \frac{5}{6} \, a b^{4} x^{6} + 2 \, a^{2} b^{3} x^{5} + \frac{5}{2} \, a^{3} b^{2} x^{4} + \frac{5}{3} \, a^{4} b x^{3} + \frac{1}{2} \, a^{5} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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