Optimal. Leaf size=28 \[ \text{Unintegrable}\left (\frac{(f+g x)^{3/2}}{a+b \log \left (c (d+e x)^n\right )},x\right ) \]
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Rubi [A] time = 0.0414031, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., 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*}
Mathematica [A] time = 1.03485, size = 0, normalized size = 0. \[ \int \frac{(f+g x)^{3/2}}{a+b \log \left (c (d+e x)^n\right )} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.723, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{a+b\ln \left ( c \left ( ex+d \right ) ^{n} \right ) } \left ( gx+f \right ) ^{{\frac{3}{2}}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \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 \left (c\right ) + 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 \left (c\right )^{2} + 2 \, a b d g \log \left (c\right ) + 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 \left (c\right )^{2} + 2 \, a b e g \log \left (c\right ) + a^{2} e g\right )} x + 2 \,{\left (b^{2} d g \log \left (c\right ) + a b d g +{\left (b^{2} e g \log \left (c\right ) + a b e g\right )} x\right )} \log \left ({\left (e x + d\right )}^{n}\right )\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (g x + f\right )}^{\frac{3}{2}}}{b \log \left ({\left (e x + d\right )}^{n} c\right ) + a}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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