Optimal. Leaf size=29 \[ \text {Int}\left (\frac {(f+g x)^m}{\left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}},x\right ) \]
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Rubi [A] time = 0.05, 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 = {} \[ \int \frac {(f+g x)^m}{\left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(f+g x)^m}{\left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}} \, dx &=\int \frac {(f+g x)^m}{\left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}} \, dx\\ \end {align*}
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Mathematica [A] time = 2.87, size = 0, normalized size = 0.00 \[ \int \frac {(f+g x)^m}{\left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.50, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sqrt {b \log \left ({\left (e x + d\right )}^{n} c\right ) + a} {\left (g x + f\right )}^{m}}{b^{2} \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + 2 \, a b \log \left ({\left (e x + d\right )}^{n} c\right ) + a^{2}}, x\right ) \]
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 \[ \int \frac {{\left (g x + f\right )}^{m}}{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{\frac {3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.64, size = 0, normalized size = 0.00 \[ \int \frac {\left (g x +f \right )^{m}}{\left (b \ln \left (c \left (e x +d \right )^{n}\right )+a \right )^{\frac {3}{2}}}\, dx \]
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 \[ \int \frac {{\left (g x + f\right )}^{m}}{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{\frac {3}{2}}}\,{d x} \]
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 \[ \int \frac {{\left (f+g\,x\right )}^m}{{\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )}^{3/2}} \,d x \]
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 \[ \text {Exception raised: HeuristicGCDFailed} \]
Verification of antiderivative is not currently implemented for this CAS.
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