Optimal. Leaf size=35 \[ \text {Int}\left (\frac {(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x},x\right ) \]
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Rubi [A]
time = 0.08, 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 {(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(h+209 x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx &=\int \frac {(h+209 x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx\\ \end {align*}
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Mathematica [A]
time = 0.51, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.26, size = 0, normalized size = 0.00 \[\int \frac {\left (i x +h \right )^{q} \left (a +b \ln \left (c \left (f x +e \right )\right )\right )^{p}}{d f x +e d}\, dx\]
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(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \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 = -0.03 \begin {gather*} \int \frac {{\left (h+i\,x\right )}^q\,{\left (a+b\,\ln \left (c\,\left (e+f\,x\right )\right )\right )}^p}{d\,e+d\,f\,x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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