Optimal. Leaf size=25 \[ \text {Int}\left (\frac {1}{\left (a+b \log \left (c \left (d+\frac {e}{f+g x}\right )^p\right )\right )^2},x\right ) \]
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Rubi [A] time = 0.01, 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 = {} \[ \int \frac {1}{\left (a+b \log \left (c \left (d+\frac {e}{f+g x}\right )^p\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{\left (a+b \log \left (c \left (d+\frac {e}{f+g x}\right )^p\right )\right )^2} \, dx &=\int \frac {1}{\left (a+b \log \left (c \left (d+\frac {e}{f+g x}\right )^p\right )\right )^2} \, dx\\ \end {align*}
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Mathematica [A] time = 0.88, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (a+b \log \left (c \left (d+\frac {e}{f+g x}\right )^p\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{b^{2} \log \left (c \left (\frac {d g x + d f + e}{g x + f}\right )^{p}\right )^{2} + 2 \, a b \log \left (c \left (\frac {d g x + d f + e}{g x + f}\right )^{p}\right ) + a^{2}}, x\right ) \]
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 \[ \int \frac {1}{{\left (b \log \left (c {\left (d + \frac {e}{g x + f}\right )}^{p}\right ) + a\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (b \ln \left (c \left (d +\frac {e}{g x +f}\right )^{p}\right )+a \right )^{2}}\, dx \]
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 \[ \frac {d g^{2} x^{2} + d f^{2} + e f + {\left (2 \, d f g + e g\right )} x}{b^{2} e g p \log \left ({\left (d g x + d f + e\right )}^{p}\right ) - b^{2} e g p \log \left ({\left (g x + f\right )}^{p}\right ) + b^{2} e g p \log \relax (c) + a b e g p} - \int \frac {2 \, d g x + 2 \, d f + e}{b^{2} e p \log \left ({\left (d g x + d f + e\right )}^{p}\right ) - b^{2} e p \log \left ({\left (g x + f\right )}^{p}\right ) + b^{2} e p \log \relax (c) + a b e p}\,{d x} \]
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 \[ \int \frac {1}{{\left (a+b\,\ln \left (c\,{\left (d+\frac {e}{f+g\,x}\right )}^p\right )\right )}^2} \,d x \]
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 \[ \int \frac {1}{\left (a + b \log {\left (c \left (d + \frac {e}{f + g x}\right )^{p} \right )}\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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