Optimal. Leaf size=29 \[ \text {Int}\left (\frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}{f+g x},x\right ) \]
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Rubi [A]
time = 0.04, 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 {\left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}{f+g x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}{f+g x} \, dx &=\int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}{f+g x} \, dx\\ \end {align*}
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Mathematica [A]
time = 1.07, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}{f+g x} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.16, size = 0, normalized size = 0.00 \[\int \frac {\left (a +b \ln \left (c \left (e x +d \right )^{n}\right )\right )^{\frac {3}{2}}}{g x +f}\, dx\]
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 {\left (a + b \log {\left (c \left (d + e x\right )^{n} \right )}\right )^{\frac {3}{2}}}{f + g x}\, 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 {{\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )}^{3/2}}{f+g\,x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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