Optimal. Leaf size=34 \[ \text{Unintegrable}\left (\frac{\sqrt{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}}{(g+h x)^{3/2}},x\right ) \]
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Rubi [A] time = 0.324221, 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 = {} \[ \int \frac{\sqrt{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}}{(g+h x)^{3/2}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\sqrt{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}}{(g+h x)^{3/2}} \, dx &=\int \frac{\sqrt{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}}{(g+h x)^{3/2}} \, dx\\ \end{align*}
Mathematica [A] time = 1.61862, size = 0, normalized size = 0. \[ \int \frac{\sqrt{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}}{(g+h x)^{3/2}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.621, size = 0, normalized size = 0. \begin{align*} \int{\sqrt{a+b\ln \left ( c \left ( d \left ( fx+e \right ) ^{p} \right ) ^{q} \right ) } \left ( hx+g \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*} \int \frac{\sqrt{b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a}}{{\left (h x + g\right )}^{\frac{3}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \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{\sqrt{b \log \left (\left ({\left (f x + e\right )}^{p} d\right )^{q} c\right ) + a}}{{\left (h x + g\right )}^{\frac{3}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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