Optimal. Leaf size=36 \[ \text{Unintegrable}\left (\frac{(a g+b g x)^2}{\left (B \log \left (\frac{e (c+d x)^2}{(a+b x)^2}\right )+A\right )^2},x\right ) \]
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Rubi [A] time = 0.211595, 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 = {} \[ \int \frac{(a g+b g x)^2}{\left (A+B \log \left (\frac{e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{(a g+b g x)^2}{\left (A+B \log \left (\frac{e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx &=\int \left (\frac{a^2 g^2}{\left (A+B \log \left (\frac{e (c+d x)^2}{(a+b x)^2}\right )\right )^2}+\frac{2 a b g^2 x}{\left (A+B \log \left (\frac{e (c+d x)^2}{(a+b x)^2}\right )\right )^2}+\frac{b^2 g^2 x^2}{\left (A+B \log \left (\frac{e (c+d x)^2}{(a+b x)^2}\right )\right )^2}\right ) \, dx\\ &=\left (a^2 g^2\right ) \int \frac{1}{\left (A+B \log \left (\frac{e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx+\left (2 a b g^2\right ) \int \frac{x}{\left (A+B \log \left (\frac{e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx+\left (b^2 g^2\right ) \int \frac{x^2}{\left (A+B \log \left (\frac{e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.460496, size = 0, normalized size = 0. \[ \int \frac{(a g+b g x)^2}{\left (A+B \log \left (\frac{e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 1., size = 0, normalized size = 0. \begin{align*} \int{ \left ( bgx+ag \right ) ^{2} \left ( A+B\ln \left ({\frac{e \left ( dx+c \right ) ^{2}}{ \left ( bx+a \right ) ^{2}}} \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{b^{3} d g^{2} x^{4} + a^{3} c g^{2} +{\left (b^{3} c g^{2} + 3 \, a b^{2} d g^{2}\right )} x^{3} + 3 \,{\left (a b^{2} c g^{2} + a^{2} b d g^{2}\right )} x^{2} +{\left (3 \, a^{2} b c g^{2} + a^{3} d g^{2}\right )} x}{2 \,{\left (2 \,{\left (b c - a d\right )} B^{2} \log \left (b x + a\right ) - 2 \,{\left (b c - a d\right )} B^{2} \log \left (d x + c\right ) -{\left (b c - a d\right )} A B -{\left (b c \log \left (e\right ) - a d \log \left (e\right )\right )} B^{2}\right )}} + \int \frac{4 \, b^{3} d g^{2} x^{3} + 3 \, a^{2} b c g^{2} + a^{3} d g^{2} + 3 \,{\left (b^{3} c g^{2} + 3 \, a b^{2} d g^{2}\right )} x^{2} + 6 \,{\left (a b^{2} c g^{2} + a^{2} b d g^{2}\right )} x}{2 \,{\left (2 \,{\left (b c - a d\right )} B^{2} \log \left (b x + a\right ) - 2 \,{\left (b c - a d\right )} B^{2} \log \left (d x + c\right ) -{\left (b c - a d\right )} A B -{\left (b c \log \left (e\right ) - a d \log \left (e\right )\right )} B^{2}\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{b^{2} g^{2} x^{2} + 2 \, a b g^{2} x + a^{2} g^{2}}{B^{2} \log \left (\frac{d^{2} e x^{2} + 2 \, c d e x + c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right )^{2} + 2 \, A B \log \left (\frac{d^{2} e x^{2} + 2 \, c d e x + c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right ) + A^{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 g x + a g\right )}^{2}}{{\left (B \log \left (\frac{{\left (d x + c\right )}^{2} e}{{\left (b x + a\right )}^{2}}\right ) + A\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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