Optimal. Leaf size=31 \[ \text{Unintegrable}\left (\frac{f+g x}{B \log \left (\frac{e (a+b x)^2}{(c+d x)^2}\right )+A},x\right ) \]
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Rubi [A] time = 0.0918307, 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 = {} \[ \int \frac{f+g x}{A+B \log \left (\frac{e (a+b x)^2}{(c+d x)^2}\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{f+g x}{A+B \log \left (\frac{e (a+b x)^2}{(c+d x)^2}\right )} \, dx &=\int \left (\frac{f}{A+B \log \left (\frac{e (a+b x)^2}{(c+d x)^2}\right )}+\frac{g x}{A+B \log \left (\frac{e (a+b x)^2}{(c+d x)^2}\right )}\right ) \, dx\\ &=f \int \frac{1}{A+B \log \left (\frac{e (a+b x)^2}{(c+d x)^2}\right )} \, dx+g \int \frac{x}{A+B \log \left (\frac{e (a+b x)^2}{(c+d x)^2}\right )} \, dx\\ \end{align*}
Mathematica [A] time = 0.126028, size = 0, normalized size = 0. \[ \int \frac{f+g x}{A+B \log \left (\frac{e (a+b x)^2}{(c+d x)^2}\right )} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.936, size = 0, normalized size = 0. \begin{align*} \int{(gx+f) \left ( A+B\ln \left ({\frac{e \left ( bx+a \right ) ^{2}}{ \left ( dx+c \right ) ^{2}}} \right ) \right ) ^{-1}}\, 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*} \int \frac{g x + f}{B \log \left (\frac{{\left (b x + a\right )}^{2} e}{{\left (d x + c\right )}^{2}}\right ) + A}\,{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{g x + f}{B \log \left (\frac{b^{2} e x^{2} + 2 \, a b e x + a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right ) + A}, 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{g x + f}{B \log \left (\frac{{\left (b x + a\right )}^{2} e}{{\left (d x + c\right )}^{2}}\right ) + A}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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