Optimal. Leaf size=26 \[ \frac{\left (a x^m+b \log ^q\left (c x^n\right )\right )^{p+1}}{p+1} \]
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Rubi [A] time = 0.171346, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 43, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.023, Rules used = {2544} \[ \frac{\left (a x^m+b \log ^q\left (c x^n\right )\right )^{p+1}}{p+1} \]
Antiderivative was successfully verified.
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Rule 2544
Rubi steps
\begin{align*} \int \frac{\left (a m x^m+b n q \log ^{-1+q}\left (c x^n\right )\right ) \left (a x^m+b \log ^q\left (c x^n\right )\right )^p}{x} \, dx &=\frac{\left (a x^m+b \log ^q\left (c x^n\right )\right )^{1+p}}{1+p}\\ \end{align*}
Mathematica [A] time = 0.0893974, size = 26, normalized size = 1. \[ \frac{\left (a x^m+b \log ^q\left (c x^n\right )\right )^{p+1}}{p+1} \]
Antiderivative was successfully verified.
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Maple [F] time = 0.5, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( am{x}^{m}+bnq \left ( \ln \left ( c{x}^{n} \right ) \right ) ^{-1+q} \right ) \left ( a{x}^{m}+b \left ( \ln \left ( c{x}^{n} \right ) \right ) ^{q} \right ) ^{p}}{x}}\, dx \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: RuntimeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.99164, size = 107, normalized size = 4.12 \begin{align*} \frac{{\left ({\left (n \log \left (x\right ) + \log \left (c\right )\right )}^{q} b + a x^{m}\right )}{\left ({\left (n \log \left (x\right ) + \log \left (c\right )\right )}^{q} b + a x^{m}\right )}^{p}}{p + 1} \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 [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: RuntimeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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