Optimal. Leaf size=60 \[ \frac{\log \left (c x^n\right )}{a \left (a x+b \log ^q\left (c x^n\right )\right )}-\frac{n (1-q) \text{CannotIntegrate}\left (\frac{1}{x \left (a x+b \log ^q\left (c x^n\right )\right )},x\right )}{a} \]
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Rubi [A] time = 0.152569, 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 = {} \[ \int \frac{n q-\log \left (c x^n\right )}{\left (a x+b \log ^q\left (c x^n\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{n q-\log \left (c x^n\right )}{\left (a x+b \log ^q\left (c x^n\right )\right )^2} \, dx &=\frac{\log \left (c x^n\right )}{a \left (a x+b \log ^q\left (c x^n\right )\right )}-\frac{(n (1-q)) \int \frac{1}{x \left (a x+b \log ^q\left (c x^n\right )\right )} \, dx}{a}\\ \end{align*}
Mathematica [A] time = 76.6005, size = 0, normalized size = 0. \[ \int \frac{n q-\log \left (c x^n\right )}{\left (a x+b \log ^q\left (c x^n\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.368, size = 0, normalized size = 0. \begin{align*} \int{\frac{nq-\ln \left ( c{x}^{n} \right ) }{ \left ( ax+b \left ( \ln \left ( c{x}^{n} \right ) \right ) ^{q} \right ) ^{2}}}\, 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*} n{\left (q - 1\right )} \int \frac{1}{a^{2} x^{2} + a b x{\left (\log \left (c\right ) + \log \left (x^{n}\right )\right )}^{q}}\,{d x} + \frac{\log \left (c\right ) + \log \left (x^{n}\right )}{a^{2} x + a b{\left (\log \left (c\right ) + \log \left (x^{n}\right )\right )}^{q}} \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{n q - \log \left (c x^{n}\right )}{a^{2} x^{2} + 2 \, a b x \log \left (c x^{n}\right )^{q} + b^{2} \log \left (c x^{n}\right )^{2 \, 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{n q - \log \left (c x^{n}\right )}{{\left (a x + b \log \left (c x^{n}\right )^{q}\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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