Optimal. Leaf size=29 \[ \text {Int}\left (\frac {(f+g x)^{3/2}}{a+b \log \left (c (d+e x)^n\right )},x\right ) \]
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Rubi [A] time = 0.04, 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 = {} \[ \int \frac {(f+g x)^{3/2}}{a+b \log \left (c (d+e x)^n\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(f+g x)^{3/2}}{a+b \log \left (c (d+e x)^n\right )} \, dx &=\int \frac {(f+g x)^{3/2}}{a+b \log \left (c (d+e x)^n\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 1.09, size = 0, normalized size = 0.00 \[ \int \frac {(f+g x)^{3/2}}{a+b \log \left (c (d+e x)^n\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.51, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (g x + f\right )}^{\frac {3}{2}}}{b \log \left ({\left (e x + d\right )}^{n} c\right ) + a}, x\right ) \]
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 \[ \int \frac {{\left (g x + f\right )}^{\frac {3}{2}}}{b \log \left ({\left (e x + d\right )}^{n} c\right ) + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.43, size = 0, normalized size = 0.00 \[ \int \frac {\left (g x +f \right )^{\frac {3}{2}}}{b \ln \left (c \left (e x +d \right )^{n}\right )+a}\, dx \]
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 \[ \frac {2 \, {\left (g^{2} x^{2} + 2 \, f g x + f^{2}\right )} \sqrt {g x + f}}{5 \, {\left (b g \log \left ({\left (e x + d\right )}^{n}\right ) + b g \log \relax (c) + a g\right )}} + \int \frac {2 \, {\left (b e g^{2} n x^{2} + 2 \, b e f g n x + b e f^{2} n\right )} \sqrt {g x + f}}{5 \, {\left (b^{2} d g \log \relax (c)^{2} + 2 \, a b d g \log \relax (c) + a^{2} d g + {\left (b^{2} e g x + b^{2} d g\right )} \log \left ({\left (e x + d\right )}^{n}\right )^{2} + {\left (b^{2} e g \log \relax (c)^{2} + 2 \, a b e g \log \relax (c) + a^{2} e g\right )} x + 2 \, {\left (b^{2} d g \log \relax (c) + a b d g + {\left (b^{2} e g \log \relax (c) + a b e g\right )} x\right )} \log \left ({\left (e x + d\right )}^{n}\right )\right )}}\,{d x} \]
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 \[ \int \frac {{\left (f+g\,x\right )}^{3/2}}{a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )} \,d x \]
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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