Optimal. Leaf size=68 \[ \frac {\log \left (a x^m+b \log ^q\left (c x^n\right )\right )}{b n q}-\frac {a m \text {Int}\left (\frac {x^{-1+m}}{a x^m+b \log ^q\left (c x^n\right )},x\right )}{b n q} \]
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Rubi [A]
time = 0.16, 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 = {}
\begin {gather*} \int \frac {\log ^{-1+q}\left (c x^n\right )}{x \left (a x^m+b \log ^q\left (c x^n\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\log ^{-1+q}\left (c x^n\right )}{x \left (a x^m+b \log ^q\left (c x^n\right )\right )} \, dx &=\frac {\log \left (a x^m+b \log ^q\left (c x^n\right )\right )}{b n q}-\frac {(a m) \int \frac {x^{-1+m}}{a x^m+b \log ^q\left (c x^n\right )} \, dx}{b n q}\\ \end {align*}
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Mathematica [A]
time = 0.09, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\log ^{-1+q}\left (c x^n\right )}{x \left (a x^m+b \log ^q\left (c x^n\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {\ln \left (c \,x^{n}\right )^{-1+q}}{x \left (a \,x^{m}+b \ln \left (c \,x^{n}\right )^{q}\right )}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {\log {\left (c x^{n} \right )}^{q - 1}}{x \left (a x^{m} + b \log {\left (c x^{n} \right )}^{q}\right )}\, dx \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [A]
time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} \int \frac {{\ln \left (c\,x^n\right )}^{q-1}}{x\,\left (a\,x^m+b\,{\ln \left (c\,x^n\right )}^q\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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