Optimal. Leaf size=28 \[ \text{Unintegrable}\left (\frac{1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )},x\right ) \]
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Rubi [A] time = 0.0424962, 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 = {} \[ \int \frac{1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx &=\int \frac{1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx\\ \end{align*}
Mathematica [A] time = 1.3744, size = 0, normalized size = 0. \[ \int \frac{1}{(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.668, 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*} -2 \, b e n \int \frac{1}{{\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 )} \sqrt{g x + f}}\,{d x} - \frac{2}{{\left (b g \log \left ({\left (e x + d\right )}^{n}\right ) + b g \log \left (c\right ) + a g\right )} \sqrt{g x + f}} \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{\sqrt{g x + f}}{a g^{2} x^{2} + 2 \, a f g x + a f^{2} +{\left (b g^{2} x^{2} + 2 \, b f g x + b f^{2}\right )} \log \left ({\left (e x + d\right )}^{n} c\right )}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\left (a + b \log{\left (c \left (d + e x\right )^{n} \right )}\right ) \left (f + g x\right )^{\frac{3}{2}}}\, dx \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{1}{{\left (g x + f\right )}^{\frac{3}{2}}{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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