Optimal. Leaf size=23 \[ -\frac{a+b \log \left (c x^n\right )}{x}-\frac{b n}{x} \]
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Rubi [A] time = 0.0129638, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {2304} \[ -\frac{a+b \log \left (c x^n\right )}{x}-\frac{b n}{x} \]
Antiderivative was successfully verified.
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Rule 2304
Rubi steps
\begin{align*} \int \frac{a+b \log \left (c x^n\right )}{x^2} \, dx &=-\frac{b n}{x}-\frac{a+b \log \left (c x^n\right )}{x}\\ \end{align*}
Mathematica [A] time = 0.001195, size = 26, normalized size = 1.13 \[ -\frac{a}{x}-\frac{b \log \left (c x^n\right )}{x}-\frac{b n}{x} \]
Antiderivative was successfully verified.
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Maple [C] time = 0.082, size = 112, normalized size = 4.9 \begin{align*} -{\frac{b\ln \left ({x}^{n} \right ) }{x}}-{\frac{ib\pi \,{\it csgn} \left ( i{x}^{n} \right ) \left ({\it csgn} \left ( ic{x}^{n} \right ) \right ) ^{2}-ib\pi \,{\it csgn} \left ( i{x}^{n} \right ){\it csgn} \left ( ic{x}^{n} \right ){\it csgn} \left ( ic \right ) -ib\pi \, \left ({\it csgn} \left ( ic{x}^{n} \right ) \right ) ^{3}+ib\pi \, \left ({\it csgn} \left ( ic{x}^{n} \right ) \right ) ^{2}{\it csgn} \left ( ic \right ) +2\,b\ln \left ( c \right ) +2\,bn+2\,a}{2\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.18859, size = 35, normalized size = 1.52 \begin{align*} -\frac{b n}{x} - \frac{b \log \left (c x^{n}\right )}{x} - \frac{a}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.961065, size = 51, normalized size = 2.22 \begin{align*} -\frac{b n \log \left (x\right ) + b n + b \log \left (c\right ) + a}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.473747, size = 24, normalized size = 1.04 \begin{align*} - \frac{a}{x} - \frac{b n \log{\left (x \right )}}{x} - \frac{b n}{x} - \frac{b \log{\left (c \right )}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17494, size = 32, normalized size = 1.39 \begin{align*} -\frac{b n \log \left (x\right )}{x} - \frac{b n + b \log \left (c\right ) + a}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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