Optimal. Leaf size=21 \[ \text {Int}\left (\frac {\log \left (a x^{-n}+b\right )}{c+d x},x\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\log \left (x^{-n} \left (a+b x^n\right )\right )}{c+d x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\log \left (x^{-n} \left (a+b x^n\right )\right )}{c+d x} \, dx &=\int \frac {\log \left (b+a x^{-n}\right )}{c+d x} \, dx\\ \end {align*}
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Mathematica [A] time = 0.50, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (x^{-n} \left (a+b x^n\right )\right )}{c+d x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.42, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \left (\frac {b x^{n} + a}{x^{n}}\right )}{d x + c}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (\frac {b x^{n} + a}{x^{n}}\right )}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.68, size = 0, normalized size = 0.00 \[ \int \frac {\ln \left (\left (b \,x^{n}+a \right ) x^{-n}\right )}{d x +c}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (\frac {b x^{n} + a}{x^{n}}\right )}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {\ln \left (\frac {a+b\,x^n}{x^n}\right )}{c+d\,x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log {\left (a x^{- n} + b \right )}}{c + d x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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