Optimal. Leaf size=103 \[ \frac{2 f \text{Unintegrable}\left (\frac{1}{\left (-\sqrt{e^2-4 d f}+e+2 f x\right ) \log \left (c (a+b x)^n\right )},x\right )}{\sqrt{e^2-4 d f}}-\frac{2 f \text{Unintegrable}\left (\frac{1}{\left (\sqrt{e^2-4 d f}+e+2 f x\right ) \log \left (c (a+b x)^n\right )},x\right )}{\sqrt{e^2-4 d f}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.199032, 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 = {} \[ \int \frac{1}{\left (d+e x+f x^2\right ) \log \left (c (a+b x)^n\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{1}{\left (d+e x+f x^2\right ) \log \left (c (a+b x)^n\right )} \, dx &=\int \left (\frac{2 f}{\sqrt{e^2-4 d f} \left (e-\sqrt{e^2-4 d f}+2 f x\right ) \log \left (c (a+b x)^n\right )}-\frac{2 f}{\sqrt{e^2-4 d f} \left (e+\sqrt{e^2-4 d f}+2 f x\right ) \log \left (c (a+b x)^n\right )}\right ) \, dx\\ &=\frac{(2 f) \int \frac{1}{\left (e-\sqrt{e^2-4 d f}+2 f x\right ) \log \left (c (a+b x)^n\right )} \, dx}{\sqrt{e^2-4 d f}}-\frac{(2 f) \int \frac{1}{\left (e+\sqrt{e^2-4 d f}+2 f x\right ) \log \left (c (a+b x)^n\right )} \, dx}{\sqrt{e^2-4 d f}}\\ \end{align*}
Mathematica [A] time = 0.565202, size = 0, normalized size = 0. \[ \int \frac{1}{\left (d+e x+f x^2\right ) \log \left (c (a+b x)^n\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 1.796, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( f{x}^{2}+ex+d \right ) \ln \left ( c \left ( bx+a \right ) ^{n} \right ) }}\, 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*} \int \frac{1}{{\left (f x^{2} + e x + d\right )} \log \left ({\left (b x + a\right )}^{n} c\right )}\,{d x} \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}{{\left (f x^{2} + e x + d\right )} \log \left ({\left (b x + a\right )}^{n} 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 (f x^{2} + e x + d\right )} \log \left ({\left (b x + a\right )}^{n} c\right )}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]