Optimal. Leaf size=71 \[ -\frac{a m \text{CannotIntegrate}\left (\frac{x^{m-1}}{\left (a x^m+b \log ^q\left (c x^n\right )\right )^3},x\right )}{b n q}-\frac{1}{2 b n q \left (a x^m+b \log ^q\left (c x^n\right )\right )^2} \]
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Rubi [A] time = 0.245109, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., 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*}
Mathematica [A] time = 1.47245, size = 0, normalized size = 0. \[ \int \frac{\log ^{-1+q}\left (c x^n\right )}{x \left (a x^m+b \log ^q\left (c x^n\right )\right )^3} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 49.67, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \ln \left ( c{x}^{n} \right ) \right ) ^{-1+q}}{x \left ( a{x}^{m}+b \left ( \ln \left ( c{x}^{n} \right ) \right ) ^{q} \right ) ^{3}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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