Optimal. Leaf size=81 \[ \frac {e \left (a x^m+b \log ^q\left (c x^n\right )\right )^{1+p}}{b n (1+p) q}+\left (d-\frac {a e m}{b n q}\right ) \text {Int}\left (x^{-1+m} \left (a x^m+b \log ^q\left (c x^n\right )\right )^p,x\right ) \]
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Rubi [A]
time = 0.17, 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 {\left (d x^m+e \log ^{-1+q}\left (c x^n\right )\right ) \left (a x^m+b \log ^q\left (c x^n\right )\right )^p}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\left (d x^m+e \log ^{-1+q}\left (c x^n\right )\right ) \left (a x^m+b \log ^q\left (c x^n\right )\right )^p}{x} \, dx &=\frac {e \left (a x^m+b \log ^q\left (c x^n\right )\right )^{1+p}}{b n (1+p) q}-\left (-d+\frac {a e m}{b n q}\right ) \int x^{-1+m} \left (a x^m+b \log ^q\left (c x^n\right )\right )^p \, dx\\ \end {align*}
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Mathematica [A]
time = 1.41, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (d x^m+e \log ^{-1+q}\left (c x^n\right )\right ) \left (a x^m+b \log ^q\left (c x^n\right )\right )^p}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.09, size = 0, normalized size = 0.00 \[\int \frac {\left (d \,x^{m}+e \ln \left (c \,x^{n}\right )^{-1+q}\right ) \left (a \,x^{m}+b \ln \left (c \,x^{n}\right )^{q}\right )^{p}}{x}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \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 [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \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 {{\left (a\,x^m+b\,{\ln \left (c\,x^n\right )}^q\right )}^p\,\left (d\,x^m+e\,{\ln \left (c\,x^n\right )}^{q-1}\right )}{x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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