Optimal. Leaf size=23 \[ \text {Int}\left (\frac {\log \left (c \left (d+e x^n\right )^p\right )}{(f+g x)^2},x\right ) \]
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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 = {} \[ \int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{(f+g x)^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{(f+g x)^2} \, dx &=\int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{(f+g x)^2} \, dx\\ \end {align*}
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Mathematica [A] time = 0.19, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{(f+g x)^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \left ({\left (e x^{n} + d\right )}^{p} c\right )}{g^{2} x^{2} + 2 \, f g x + f^{2}}, x\right ) \]
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 \[ \int \frac {\log \left ({\left (e x^{n} + d\right )}^{p} c\right )}{{\left (g x + f\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.37, size = 0, normalized size = 0.00 \[ \int \frac {\ln \left (c \left (e \,x^{n}+d \right )^{p}\right )}{\left (g x +f \right )^{2}}\, dx \]
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 \[ -d n p \int \frac {1}{d g^{2} x^{2} + d f g x + {\left (e g^{2} x^{2} + e f g x\right )} x^{n}}\,{d x} - \frac {n p \log \left (g x + f\right )}{f g} - \frac {f \log \left ({\left (e x^{n} + d\right )}^{p}\right ) + f \log \relax (c) - {\left (g n p x + f n p\right )} \log \relax (x)}{f g^{2} x + f^{2} g} \]
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 \[ \int \frac {\ln \left (c\,{\left (d+e\,x^n\right )}^p\right )}{{\left (f+g\,x\right )}^2} \,d x \]
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 \[ \int \frac {\log {\left (c \left (d + e x^{n}\right )^{p} \right )}}{\left (f + g x\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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