Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{1}{\left (d+e x^3\right )^2 \left (a+b \log \left (c x^n\right )\right )^2},x\right ) \]
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Rubi [A] time = 0.0301049, 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 = {} \[ \int \frac{1}{\left (d+e x^3\right )^2 \left (a+b \log \left (c x^n\right )\right )^2} \, dx \]
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 )^2} \, dx &=\int \frac{1}{\left (d+e x^3\right )^2 \left (a+b \log \left (c x^n\right )\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 25.5766, size = 0, normalized size = 0. \[ \int \frac{1}{\left (d+e x^3\right )^2 \left (a+b \log \left (c x^n\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 2.035, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( e{x}^{3}+d \right ) ^{2} \left ( a+b\ln \left ( c{x}^{n} \right ) \right ) ^{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*} -\frac{x}{{\left (b^{2} e^{2} n \log \left (c\right ) + a b e^{2} n\right )} x^{6} + b^{2} d^{2} n \log \left (c\right ) + a b d^{2} n + 2 \,{\left (b^{2} d e n \log \left (c\right ) + a b d e n\right )} x^{3} +{\left (b^{2} e^{2} n x^{6} + 2 \, b^{2} d e n x^{3} + b^{2} d^{2} n\right )} \log \left (x^{n}\right )} - \int \frac{5 \, e x^{3} - d}{{\left (b^{2} e^{3} n \log \left (c\right ) + a b e^{3} n\right )} x^{9} + 3 \,{\left (b^{2} d e^{2} n \log \left (c\right ) + a b d e^{2} n\right )} x^{6} + b^{2} d^{3} n \log \left (c\right ) + a b d^{3} n + 3 \,{\left (b^{2} d^{2} e n \log \left (c\right ) + a b d^{2} e n\right )} x^{3} +{\left (b^{2} e^{3} n x^{9} + 3 \, b^{2} d e^{2} n x^{6} + 3 \, b^{2} d^{2} e n x^{3} + b^{2} d^{3} n\right )} \log \left (x^{n}\right )}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{a^{2} e^{2} x^{6} + 2 \, a^{2} d e x^{3} + a^{2} d^{2} +{\left (b^{2} e^{2} x^{6} + 2 \, b^{2} d e x^{3} + b^{2} d^{2}\right )} \log \left (c x^{n}\right )^{2} + 2 \,{\left (a b e^{2} x^{6} + 2 \, a b d e x^{3} + a b d^{2}\right )} \log \left (c x^{n}\right )}, x\right ) \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{1}{{\left (e x^{3} + d\right )}^{2}{\left (b \log \left (c x^{n}\right ) + a\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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