Optimal. Leaf size=25 \[ \text {Int}\left (\frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )^2},x\right ) \]
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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 = {} \[ \int \frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )^2} \, dx &=\int \frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )^2} \, dx\\ \end {align*}
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Mathematica [A] time = 14.49, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (d+e x^2\right )^2 \left (a+b \log \left (c x^n\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{a^{2} e^{2} x^{4} + 2 \, a^{2} d e x^{2} + a^{2} d^{2} + {\left (b^{2} e^{2} x^{4} + 2 \, b^{2} d e x^{2} + b^{2} d^{2}\right )} \log \left (c x^{n}\right )^{2} + 2 \, {\left (a b e^{2} x^{4} + 2 \, a b d e x^{2} + a b d^{2}\right )} \log \left (c x^{n}\right )}, x\right ) \]
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 \[ \int \frac {1}{{\left (e x^{2} + d\right )}^{2} {\left (b \log \left (c x^{n}\right ) + a\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 3.52, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (e \,x^{2}+d \right )^{2} \left (b \ln \left (c \,x^{n}\right )+a \right )^{2}}\, dx \]
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 \[ -\frac {x}{b^{2} d^{2} n \log \relax (c) + a b d^{2} n + {\left (b^{2} e^{2} n \log \relax (c) + a b e^{2} n\right )} x^{4} + 2 \, {\left (b^{2} d e n \log \relax (c) + a b d e n\right )} x^{2} + {\left (b^{2} e^{2} n x^{4} + 2 \, b^{2} d e n x^{2} + b^{2} d^{2} n\right )} \log \left (x^{n}\right )} - \int \frac {3 \, e x^{2} - d}{{\left (b^{2} e^{3} n \log \relax (c) + a b e^{3} n\right )} x^{6} + b^{2} d^{3} n \log \relax (c) + a b d^{3} n + 3 \, {\left (b^{2} d e^{2} n \log \relax (c) + a b d e^{2} n\right )} x^{4} + 3 \, {\left (b^{2} d^{2} e n \log \relax (c) + a b d^{2} e n\right )} x^{2} + {\left (b^{2} e^{3} n x^{6} + 3 \, b^{2} d e^{2} n x^{4} + 3 \, b^{2} d^{2} e n x^{2} + b^{2} d^{3} n\right )} \log \left (x^{n}\right )}\,{d x} \]
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 \[ \int \frac {1}{{\left (e\,x^2+d\right )}^2\,{\left (a+b\,\ln \left (c\,x^n\right )\right )}^2} \,d x \]
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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