Optimal. Leaf size=33 \[ \text {Int}\left (\frac {(g+h x)^{3/2}}{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )},x\right ) \]
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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 = {}
\begin {gather*} \int \frac {(g+h x)^{3/2}}{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(g+h x)^{3/2}}{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )} \, dx &=\int \frac {(g+h x)^{3/2}}{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )} \, dx\\ \end {align*}
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Mathematica [A]
time = 0.76, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(g+h x)^{3/2}}{a+b \log \left (c \left (d (e+f x)^p\right )^q\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.22, size = 0, normalized size = 0.00 \[\int \frac {\left (h x +g \right )^{\frac {3}{2}}}{a +b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {{\left (g+h\,x\right )}^{3/2}}{a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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