Optimal. Leaf size=31 \[ \text{Unintegrable}\left (\frac{1}{(f+g x) \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2},x\right ) \]
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Rubi [A] time = 0.0696734, 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 = {} \[ \int \frac{1}{(f+g x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{(f+g x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2} \, dx &=\int \frac{1}{(f+g x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 2.50478, size = 0, normalized size = 0. \[ \int \frac{1}{(f+g x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 1.425, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{gx+f} \left ( A+B\ln \left ({\frac{e \left ( bx+a \right ) }{dx+c}} \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 d x^{2} + a c +{\left (b c + a d\right )} x}{{\left (b c f - a d f\right )} A B +{\left (b c f \log \left (e\right ) - a d f \log \left (e\right )\right )} B^{2} +{\left ({\left (b c g - a d g\right )} A B +{\left (b c g \log \left (e\right ) - a d g \log \left (e\right )\right )} B^{2}\right )} x +{\left ({\left (b c g - a d g\right )} B^{2} x +{\left (b c f - a d f\right )} B^{2}\right )} \log \left (b x + a\right ) -{\left ({\left (b c g - a d g\right )} B^{2} x +{\left (b c f - a d f\right )} B^{2}\right )} \log \left (d x + c\right )} + \int \frac{b d g x^{2} + 2 \, b d f x + b c f +{\left (d f - c g\right )} a}{{\left (b c f^{2} - a d f^{2}\right )} A B +{\left (b c f^{2} \log \left (e\right ) - a d f^{2} \log \left (e\right )\right )} B^{2} +{\left ({\left (b c g^{2} - a d g^{2}\right )} A B +{\left (b c g^{2} \log \left (e\right ) - a d g^{2} \log \left (e\right )\right )} B^{2}\right )} x^{2} + 2 \,{\left ({\left (b c f g - a d f g\right )} A B +{\left (b c f g \log \left (e\right ) - a d f g \log \left (e\right )\right )} B^{2}\right )} x +{\left ({\left (b c g^{2} - a d g^{2}\right )} B^{2} x^{2} + 2 \,{\left (b c f g - a d f g\right )} B^{2} x +{\left (b c f^{2} - a d f^{2}\right )} B^{2}\right )} \log \left (b x + a\right ) -{\left ({\left (b c g^{2} - a d g^{2}\right )} B^{2} x^{2} + 2 \,{\left (b c f g - a d f g\right )} B^{2} x +{\left (b c f^{2} - a d f^{2}\right )} B^{2}\right )} \log \left (d x + c\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{1}{A^{2} g x + A^{2} f +{\left (B^{2} g x + B^{2} f\right )} \log \left (\frac{b e x + a e}{d x + c}\right )^{2} + 2 \,{\left (A B g x + A B f\right )} \log \left (\frac{b e x + a e}{d x + c}\right )}, 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{1}{{\left (g x + f\right )}{\left (B \log \left (\frac{{\left (b x + a\right )} e}{d x + c}\right ) + A\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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