Optimal. Leaf size=11 \[ x (a+b x)^{m+1} \]
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Rubi [A] time = 0.0022903, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {34} \[ x (a+b x)^{m+1} \]
Antiderivative was successfully verified.
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Rule 34
Rubi steps
\begin{align*} \int (a+b x)^m (a+b (2+m) x) \, dx &=x (a+b x)^{1+m}\\ \end{align*}
Mathematica [A] time = 0.0108006, size = 11, normalized size = 1. \[ x (a+b x)^{m+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 12, normalized size = 1.1 \begin{align*} x \left ( bx+a \right ) ^{1+m} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.71111, size = 36, normalized size = 3.27 \begin{align*}{\left (b x^{2} + a x\right )}{\left (b x + a\right )}^{m} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.251909, size = 20, normalized size = 1.82 \begin{align*} a x \left (a + b x\right )^{m} + b x^{2} \left (a + b x\right )^{m} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.06955, size = 31, normalized size = 2.82 \begin{align*}{\left (b x + a\right )}^{m} b x^{2} +{\left (b x + a\right )}^{m} a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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