Optimal. Leaf size=61 \[ \frac {\log \left (c x^n\right )}{a \left (a x+b \log ^q\left (c x^n\right )\right )}-\frac {n (1-q) \text {Int}\left (\frac {1}{x \left (a x+b \log ^q\left (c x^n\right )\right )},x\right )}{a} \]
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Rubi [A]
time = 0.10, 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 {n q-\log \left (c x^n\right )}{\left (a x+b \log ^q\left (c x^n\right )\right )^2} \, dx \end {gather*}
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*}
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Mathematica [A]
time = 85.79, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {n q-\log \left (c x^n\right )}{\left (a x+b \log ^q\left (c x^n\right )\right )^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {n q -\ln \left (c \,x^{n}\right )}{\left (a x +b \ln \left (c \,x^{n}\right )^{q}\right )^{2}}\, dx\]
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 {n q - \log {\left (c x^{n} \right )}}{\left (a x + b \log {\left (c x^{n} \right )}^{q}\right )^{2}}\, 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 = -0.02 \begin {gather*} \int -\frac {\ln \left (c\,x^n\right )-n\,q}{{\left (b\,{\ln \left (c\,x^n\right )}^q+a\,x\right )}^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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