Optimal. Leaf size=26 \[ \text {Int}\left (\frac {a+b \log \left (c x^n\right )}{x^2 \left (d+e x^r\right )},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.04, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {a+b \log \left (c x^n\right )}{x^2 \left (d+e x^r\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {a+b \log \left (c x^n\right )}{x^2 \left (d+e x^r\right )} \, dx &=\int \frac {a+b \log \left (c x^n\right )}{x^2 \left (d+e x^r\right )} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] Leaf count is larger than twice the leaf count of optimal. \(83\) vs. \(2(26)=52\).
time = 0.06, size = 83, normalized size = 3.19 \begin {gather*} -\frac {b n \, _3F_2\left (1,-\frac {1}{r},-\frac {1}{r};1-\frac {1}{r},1-\frac {1}{r};-\frac {e x^r}{d}\right )+\, _2F_1\left (1,-\frac {1}{r};\frac {-1+r}{r};-\frac {e x^r}{d}\right ) \left (a+b \log \left (c x^n\right )\right )}{d x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.05, size = 0, normalized size = 0.00 \[\int \frac {a +b \ln \left (c \,x^{n}\right )}{x^{2} \left (d +e \,x^{r}\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {a + b \log {\left (c x^{n} \right )}}{x^{2} \left (d + e x^{r}\right )}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {a+b\,\ln \left (c\,x^n\right )}{x^2\,\left (d+e\,x^r\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________