Optimal. Leaf size=42 \[ \text {Int}\left (\frac {\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{x \log ^2\left (i \left (j (h x)^t\right )^u\right )},x\right ) \]
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Rubi [A]
time = 0.30, 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 {\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{x \log ^2\left (i \left (j (h x)^t\right )^u\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{x \log ^2\left (61 \left (j (h x)^t\right )^u\right )} \, dx &=\int \frac {\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{x \log ^2\left (61 \left (j (h x)^t\right )^u\right )} \, dx\\ \end {align*}
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Mathematica [A]
time = 1.51, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{x \log ^2\left (i \left (j (h x)^t\right )^u\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 1.06, size = 0, normalized size = 0.00 \[\int \frac {\ln \left (e \left (f \left (b x +a \right )^{p} \left (d x +c \right )^{q}\right )^{r}\right )}{x \ln \left (i \left (j \left (h x \right )^{t}\right )^{u}\right )^{2}}\, dx\]
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 [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 [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 (e\,{\left (f\,{\left (a+b\,x\right )}^p\,{\left (c+d\,x\right )}^q\right )}^r\right )}{x\,{\ln \left (i\,{\left (j\,{\left (h\,x\right )}^t\right )}^u\right )}^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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