Optimal. Leaf size=66 \[ \frac{\log \left (a x^m+b \log ^2\left (c x^n\right )\right )}{2 b n}-\frac{a m \text{CannotIntegrate}\left (\frac{x^{m-1}}{a x^m+b \log ^2\left (c x^n\right )},x\right )}{2 b n} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.191758, 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 = {} \[ \int \frac{\log \left (c x^n\right )}{x \left (a x^m+b \log ^2\left (c x^n\right )\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\log \left (c x^n\right )}{x \left (a x^m+b \log ^2\left (c x^n\right )\right )} \, dx &=\frac{\log \left (a x^m+b \log ^2\left (c x^n\right )\right )}{2 b n}-\frac{(a m) \int \frac{x^{-1+m}}{a x^m+b \log ^2\left (c x^n\right )} \, dx}{2 b n}\\ \end{align*}
Mathematica [A] time = 1.40854, size = 0, normalized size = 0. \[ \int \frac{\log \left (c x^n\right )}{x \left (a x^m+b \log ^2\left (c x^n\right )\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 1.777, size = 0, normalized size = 0. \begin{align*} \int{\frac{\ln \left ( c{x}^{n} \right ) }{x \left ( a{x}^{m}+b \left ( \ln \left ( c{x}^{n} \right ) \right ) ^{2} \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{\log \left (c x^{n}\right )}{{\left (b \log \left (c x^{n}\right )^{2} + a x^{m}\right )} x}\,{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{\log \left (c x^{n}\right )}{b x \log \left (c x^{n}\right )^{2} + a x x^{m}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log{\left (c x^{n} \right )}}{x \left (a x^{m} + b \log{\left (c x^{n} \right )}^{2}\right )}\, dx \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{\log \left (c x^{n}\right )}{{\left (b \log \left (c x^{n}\right )^{2} + a x^{m}\right )} x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]