Optimal. Leaf size=51 \[ \frac{\text{Unintegrable}\left (\frac{1}{x \log \left (c (a+b x)^n\right )},x\right )}{d}-\frac{e \text{Unintegrable}\left (\frac{1}{(d+e x) \log \left (c (a+b x)^n\right )},x\right )}{d} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.10989, 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 = {} \[ \int \frac{1}{\left (d x+e x^2\right ) \log \left (c (a+b x)^n\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{1}{\left (d x+e x^2\right ) \log \left (c (a+b x)^n\right )} \, dx &=\int \frac{1}{x (d+e x) \log \left (c (a+b x)^n\right )} \, dx\\ &=\int \left (\frac{1}{d x \log \left (c (a+b x)^n\right )}-\frac{e}{d (d+e x) \log \left (c (a+b x)^n\right )}\right ) \, dx\\ &=\frac{\int \frac{1}{x \log \left (c (a+b x)^n\right )} \, dx}{d}-\frac{e \int \frac{1}{(d+e x) \log \left (c (a+b x)^n\right )} \, dx}{d}\\ \end{align*}
Mathematica [A] time = 0.625283, size = 0, normalized size = 0. \[ \int \frac{1}{\left (d x+e x^2\right ) \log \left (c (a+b x)^n\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.825, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( e{x}^{2}+dx \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 (e x^{2} + d x\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 (e x^{2} + d x\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 [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \left (d + e x\right ) \log{\left (c \left (a + b x\right )^{n} \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{1}{{\left (e x^{2} + d x\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]