Optimal. Leaf size=35 \[ \text {Int}\left (\frac {(a+b \log (c (e+f x)))^p}{(h+i x)^3 (d e+d f x)},x\right ) \]
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Rubi [A] time = 0.13, 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 = {} \[ \int \frac {(a+b \log (c (e+f x)))^p}{(d e+d f x) (h+i x)^3} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(a+b \log (c (e+f x)))^p}{(h+216 x)^3 (d e+d f x)} \, dx &=\int \frac {(a+b \log (c (e+f x)))^p}{(h+216 x)^3 (d e+d f x)} \, dx\\ \end {align*}
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Mathematica [A] time = 3.85, size = 0, normalized size = 0.00 \[ \int \frac {(a+b \log (c (e+f x)))^p}{(d e+d f x) (h+i x)^3} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.50, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (b \log \left (c f x + c e\right ) + a\right )}^{p}}{d f i^{3} x^{4} + d e h^{3} + {\left (3 \, d f h i^{2} + d e i^{3}\right )} x^{3} + 3 \, {\left (d f h^{2} i + d e h i^{2}\right )} x^{2} + {\left (d f h^{3} + 3 \, d e h^{2} i\right )} x}, x\right ) \]
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 \[ \int \frac {{\left (b \log \left ({\left (f x + e\right )} c\right ) + a\right )}^{p}}{{\left (d f x + d e\right )} {\left (i x + h\right )}^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.50, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \ln \left (\left (f x +e \right ) c \right )+a \right )^{p}}{\left (d f x +d e \right ) \left (i x +h \right )^{3}}\, dx \]
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 \[ \int \frac {{\left (b \log \left ({\left (f x + e\right )} c\right ) + a\right )}^{p}}{{\left (d f x + d e\right )} {\left (i x + h\right )}^{3}}\,{d x} \]
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 \[ \int \frac {{\left (a+b\,\ln \left (c\,\left (e+f\,x\right )\right )\right )}^p}{{\left (h+i\,x\right )}^3\,\left (d\,e+d\,f\,x\right )} \,d x \]
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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