Optimal. Leaf size=72 \[ -\frac {a m \text {Int}\left (\frac {x^{m-1}}{\left (a x^m+b \log ^q\left (c x^n\right )\right )^3},x\right )}{b n q}-\frac {1}{2 b n q \left (a x^m+b \log ^q\left (c x^n\right )\right )^2} \]
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Rubi [A] time = 0.25, 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 = {} \[ \int \frac {\log ^{-1+q}\left (c x^n\right )}{x \left (a x^m+b \log ^q\left (c x^n\right )\right )^3} \, dx \]
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 )^3} \, dx &=-\frac {1}{2 b n q \left (a x^m+b \log ^q\left (c x^n\right )\right )^2}-\frac {(a m) \int \frac {x^{-1+m}}{\left (a x^m+b \log ^q\left (c x^n\right )\right )^3} \, dx}{b n q}\\ \end {align*}
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Mathematica [A] time = 1.63, size = 0, normalized size = 0.00 \[ \int \frac {\log ^{-1+q}\left (c x^n\right )}{x \left (a x^m+b \log ^q\left (c x^n\right )\right )^3} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.08, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \left (c x^{n}\right )^{q - 1}}{3 \, a b^{2} x x^{m} \log \left (c x^{n}\right )^{2 \, q} + 3 \, a^{2} b x x^{2 \, m} \log \left (c x^{n}\right )^{q} + a^{3} x x^{3 \, m} + b^{3} x \log \left (c x^{n}\right )^{3 \, q}}, x\right ) \]
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 \[ \int \frac {\log \left (c x^{n}\right )^{q - 1}}{{\left (a x^{m} + b \log \left (c x^{n}\right )^{q}\right )}^{3} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 121.28, size = 0, normalized size = 0.00 \[ \int \frac {\ln \left (c \,x^{n}\right )^{q -1}}{\left (a \,x^{m}+b \ln \left (c \,x^{n}\right )^{q}\right )^{3} x}\, dx \]
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 \[ \text {result too large to display} \]
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 \[ \int \frac {{\ln \left (c\,x^n\right )}^{q-1}}{x\,{\left (a\,x^m+b\,{\ln \left (c\,x^n\right )}^q\right )}^3} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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