Optimal. Leaf size=26 \[ \frac{(c x)^{m+1} \left (b x^n\right )^p}{c (m+n p+1)} \]
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Rubi [A] time = 0.0053109, antiderivative size = 22, normalized size of antiderivative = 0.85, number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231, Rules used = {15, 20, 30} \[ \frac{x (c x)^m \left (b x^n\right )^p}{m+n p+1} \]
Antiderivative was successfully verified.
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Rule 15
Rule 20
Rule 30
Rubi steps
\begin{align*} \int (c x)^m \left (b x^n\right )^p \, dx &=\left (x^{-n p} \left (b x^n\right )^p\right ) \int x^{n p} (c x)^m \, dx\\ &=\left (x^{-m-n p} (c x)^m \left (b x^n\right )^p\right ) \int x^{m+n p} \, dx\\ &=\frac{x (c x)^m \left (b x^n\right )^p}{1+m+n p}\\ \end{align*}
Mathematica [A] time = 0.003365, size = 22, normalized size = 0.85 \[ \frac{x (c x)^m \left (b x^n\right )^p}{m+n p+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 23, normalized size = 0.9 \begin{align*}{\frac{x \left ( cx \right ) ^{m} \left ( b{x}^{n} \right ) ^{p}}{np+m+1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01598, size = 38, normalized size = 1.46 \begin{align*} \frac{b^{p} c^{m} x e^{\left (m \log \left (x\right ) + p \log \left (x^{n}\right )\right )}}{n p + m + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.71931, size = 88, normalized size = 3.38 \begin{align*} \frac{x e^{\left (n p \log \left (x\right ) + p \log \left (b\right ) + m \log \left (c\right ) + m \log \left (x\right )\right )}}{n p + m + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18513, size = 39, normalized size = 1.5 \begin{align*} \frac{x e^{\left (n p \log \left (x\right ) + p \log \left (b\right ) + m \log \left (c\right ) + m \log \left (x\right )\right )}}{n p + m + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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