Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\frac{a+b \log \left (c x^n\right )}{x^3 \left (d+e x^r\right )},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0640177, 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 = {} \[ \int \frac{a+b \log \left (c x^n\right )}{x^3 \left (d+e x^r\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{a+b \log \left (c x^n\right )}{x^3 \left (d+e x^r\right )} \, dx &=\int \frac{a+b \log \left (c x^n\right )}{x^3 \left (d+e x^r\right )} \, dx\\ \end{align*}
Mathematica [A] time = 0.104514, size = 86, normalized size = 3.44 \[ -\frac{b n \, _3F_2\left (1,-\frac{2}{r},-\frac{2}{r};1-\frac{2}{r},1-\frac{2}{r};-\frac{e x^r}{d}\right )+2 \, _2F_1\left (1,-\frac{2}{r};\frac{r-2}{r};-\frac{e x^r}{d}\right ) \left (a+b \log \left (c x^n\right )\right )}{4 d x^2} \]
Warning: Unable to verify antiderivative.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.706, size = 0, normalized size = 0. \begin{align*} \int{\frac{a+b\ln \left ( c{x}^{n} \right ) }{{x}^{3} \left ( d+e{x}^{r} \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{b \log \left (c x^{n}\right ) + a}{{\left (e x^{r} + d\right )} x^{3}}\,{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{b \log \left (c x^{n}\right ) + a}{e x^{3} x^{r} + d x^{3}}, 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{a + b \log{\left (c x^{n} \right )}}{x^{3} \left (d + e x^{r}\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{b \log \left (c x^{n}\right ) + a}{{\left (e x^{r} + d\right )} x^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]