Optimal. Leaf size=36 \[ \text{Unintegrable}\left (\frac{\left (a+b \log \left (c (d+e x)^n\right )\right )^2 \left (f+g \log \left (h (i+j x)^m\right )\right )}{x^2},x\right ) \]
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Rubi [A] time = 0.0396986, 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 = {} \[ \int \frac{\left (a+b \log \left (c (d+e x)^n\right )\right )^2 \left (f+g \log \left (h (i+j x)^m\right )\right )}{x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\left (a+b \log \left (c (d+e x)^n\right )\right )^2 \left (f+g \log \left (h (396+j x)^m\right )\right )}{x^2} \, dx &=\int \frac{\left (a+b \log \left (c (d+e x)^n\right )\right )^2 \left (f+g \log \left (h (396+j x)^m\right )\right )}{x^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.865298, size = 0, normalized size = 0. \[ \int \frac{\left (a+b \log \left (c (d+e x)^n\right )\right )^2 \left (f+g \log \left (h (i+j x)^m\right )\right )}{x^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 1.424, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( a+b\ln \left ( c \left ( ex+d \right ) ^{n} \right ) \right ) ^{2} \left ( f+g\ln \left ( h \left ( jx+i \right ) ^{m} \right ) \right ) }{{x}^{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*} -2 \, a b e f n{\left (\frac{\log \left (e x + d\right )}{d} - \frac{\log \left (x\right )}{d}\right )} - \frac{2 \, a b f \log \left ({\left (e x + d\right )}^{n} c\right )}{x} - \frac{a^{2} f}{x} + \int \frac{{\left (g \log \left (h\right ) + f\right )} b^{2} \log \left ({\left (e x + d\right )}^{n}\right )^{2} +{\left (g \log \left (h\right ) + f\right )} b^{2} \log \left (c\right )^{2} + 2 \, a b g \log \left (c\right ) \log \left (h\right ) + a^{2} g \log \left (h\right ) + 2 \,{\left ({\left (g \log \left (h\right ) + f\right )} b^{2} \log \left (c\right ) + a b g \log \left (h\right )\right )} \log \left ({\left (e x + d\right )}^{n}\right ) +{\left (b^{2} g \log \left ({\left (e x + d\right )}^{n}\right )^{2} + b^{2} g \log \left (c\right )^{2} + 2 \, a b g \log \left (c\right ) + a^{2} g + 2 \,{\left (b^{2} g \log \left (c\right ) + a b g\right )} \log \left ({\left (e x + d\right )}^{n}\right )\right )} \log \left ({\left (j x + i\right )}^{m}\right )}{x^{2}}\,{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{b^{2} f \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + 2 \, a b f \log \left ({\left (e x + d\right )}^{n} c\right ) + a^{2} f +{\left (b^{2} g \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + 2 \, a b g \log \left ({\left (e x + d\right )}^{n} c\right ) + a^{2} g\right )} \log \left ({\left (j x + i\right )}^{m} h\right )}{x^{2}}, 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{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{2}{\left (g \log \left ({\left (j x + i\right )}^{m} h\right ) + f\right )}}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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