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 = 0.11, 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 = {} \[ \int \frac {(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx \]
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 = 0.62, size = 0, normalized size = 0.00 \[ \int \frac {(h+i x)^q (a+b \log (c (e+f x)))^p}{d e+d f x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.49, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (i x + h\right )}^{q} {\left (b \log \left (c f x + c e\right ) + a\right )}^{p}}{d f x + d e}, x\right ) \]
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 \[ \text {Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.88, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \ln \left (\left (f x +e \right ) c \right )+a \right )^{p} \left (i x +h \right )^{q}}{d f x +d e}\, dx \]
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 \[ \int \frac {{\left (i x + h\right )}^{q} {\left (b \log \left ({\left (f x + e\right )} c\right ) + a\right )}^{p}}{d f x + d e}\,{d x} \]
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 \[ \int \frac {{\left (h+i\,x\right )}^q\,{\left (a+b\,\ln \left (c\,\left (e+f\,x\right )\right )\right )}^p}{d\,e+d\,f\,x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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