Optimal. Leaf size=34 \[ \text{Unintegrable}\left (\frac{1}{(a g+b g x) \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0808696, 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 = {} \[ \int \frac{1}{(a g+b g x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{1}{(a g+b g x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2} \, dx &=\int \frac{1}{(a g+b g x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.618128, size = 0, normalized size = 0. \[ \int \frac{1}{(a g+b g x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 1.042, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{bgx+ag} \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.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} d \int \frac{1}{{\left (b c g - a d g\right )} B^{2} \log \left (b x + a\right ) -{\left (b c g - a d g\right )} B^{2} \log \left (d x + c\right ) +{\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}}\,{d x} - \frac{d x + c}{{\left (b c g - a d g\right )} B^{2} \log \left (b x + a\right ) -{\left (b c g - a d g\right )} B^{2} \log \left (d x + c\right ) +{\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{A^{2} b g x + A^{2} a g +{\left (B^{2} b g x + B^{2} a g\right )} \log \left (\frac{b e x + a e}{d x + c}\right )^{2} + 2 \,{\left (A B b g x + A B a g\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.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b g x + a g\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.
[In]
[Out]