Optimal. Leaf size=27 \[ \frac{\left (a+b x^{m+1}\right )^{n+1}}{b (m+1) (n+1)} \]
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Rubi [A] time = 0.0096207, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {261} \[ \frac{\left (a+b x^{m+1}\right )^{n+1}}{b (m+1) (n+1)} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^m \left (a+b x^{1+m}\right )^n \, dx &=\frac{\left (a+b x^{1+m}\right )^{1+n}}{b (1+m) (1+n)}\\ \end{align*}
Mathematica [A] time = 0.0095069, size = 27, normalized size = 1. \[ \frac{\left (a+b x^{m+1}\right )^{n+1}}{b (m+1) (n+1)} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.024, size = 60, normalized size = 2.2 \begin{align*}{\frac{a{{\rm e}^{n\ln \left ( a+bx{{\rm e}^{m\ln \left ( x \right ) }} \right ) }}}{b \left ( nm+m+n+1 \right ) }}+{\frac{x{{\rm e}^{m\ln \left ( x \right ) }}{{\rm e}^{n\ln \left ( a+bx{{\rm e}^{m\ln \left ( x \right ) }} \right ) }}}{nm+m+n+1}} \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 = 1.36694, size = 85, normalized size = 3.15 \begin{align*} \frac{{\left (b x^{m + 1} + a\right )}{\left (b x^{m + 1} + a\right )}^{n}}{b m +{\left (b m + b\right )} n + b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12034, size = 36, normalized size = 1.33 \begin{align*} \frac{{\left (b x^{m + 1} + a\right )}^{n + 1}}{b{\left (m + 1\right )}{\left (n + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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