Optimal. Leaf size=25 \[ \text {Int}\left (\frac {1}{\left (d+e x^3\right )^2 \left (a+b \log \left (c x^n\right )\right )},x\right ) \]
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Rubi [A] time = 0.03, 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 = {} \[ \int \frac {1}{\left (d+e x^3\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{\left (d+e x^3\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx &=\int \frac {1}{\left (d+e x^3\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 5.63, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (d+e x^3\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{a e^{2} x^{6} + 2 \, a d e x^{3} + a d^{2} + {\left (b e^{2} x^{6} + 2 \, b d e x^{3} + b d^{2}\right )} \log \left (c x^{n}\right )}, x\right ) \]
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 \[ \int \frac {1}{{\left (e x^{3} + d\right )}^{2} {\left (b \log \left (c x^{n}\right ) + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.68, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (e \,x^{3}+d \right )^{2} \left (b \ln \left (c \,x^{n}\right )+a \right )}\, dx \]
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 \[ \int \frac {1}{{\left (e x^{3} + d\right )}^{2} {\left (b \log \left (c x^{n}\right ) + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {1}{{\left (e\,x^3+d\right )}^2\,\left (a+b\,\ln \left (c\,x^n\right )\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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