Optimal. Leaf size=18 \[ a x+b x \log \left (c x^n\right )-b n x \]
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Rubi [A] time = 0.005548, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {2295} \[ a x+b x \log \left (c x^n\right )-b n x \]
Antiderivative was successfully verified.
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Rule 2295
Rubi steps
\begin{align*} \int \left (a+b \log \left (c x^n\right )\right ) \, dx &=a x+b \int \log \left (c x^n\right ) \, dx\\ &=a x-b n x+b x \log \left (c x^n\right )\\ \end{align*}
Mathematica [A] time = 0.000665, size = 18, normalized size = 1. \[ a x+b x \log \left (c x^n\right )-b n x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.038, size = 19, normalized size = 1.1 \begin{align*} ax-bnx+bx\ln \left ( c{x}^{n} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10327, size = 24, normalized size = 1.33 \begin{align*} -b n x + b x \log \left (c x^{n}\right ) + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.793783, size = 55, normalized size = 3.06 \begin{align*} b n x \log \left (x\right ) + b x \log \left (c\right ) -{\left (b n - a\right )} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.239296, size = 19, normalized size = 1.06 \begin{align*} a x + b \left (n x \log{\left (x \right )} - n x + x \log{\left (c \right )}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17849, size = 27, normalized size = 1.5 \begin{align*}{\left (n x \log \left (x\right ) - n x + x \log \left (c\right )\right )} b + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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