Optimal. Leaf size=35 \[ \text {Int}\left (\frac {\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}}{(g+h x)^{3/2}},x\right ) \]
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Rubi [A]
time = 0.20, 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 {\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}}{(g+h x)^{3/2}} \, dx \end {gather*}
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*}
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Mathematica [A]
time = 0.84, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )}}{(g+h x)^{3/2}} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.20, size = 0, normalized size = 0.00 \[\int \frac {\sqrt {a +b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )}}{\left (h x +g \right )^{\frac {3}{2}}}\, dx\]
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 [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {a + b \log {\left (c \left (d \left (e + f x\right )^{p}\right )^{q} \right )}}}{\left (g + h x\right )^{\frac {3}{2}}}\, dx \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 {\sqrt {a+b\,\ln \left (c\,{\left (d\,{\left (e+f\,x\right )}^p\right )}^q\right )}}{{\left (g+h\,x\right )}^{3/2}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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