Optimal. Leaf size=28 \[ \text {Int}\left (\frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )}{\left (d+e x^r\right )^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.05, 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 {(f x)^m \left (a+b \log \left (c x^n\right )\right )}{\left (d+e x^r\right )^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )}{\left (d+e x^r\right )^2} \, dx &=\int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )}{\left (d+e x^r\right )^2} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] Leaf count is larger than twice the leaf count of optimal. \(177\) vs. \(2(28)=56\).
time = 0.25, size = 177, normalized size = 6.32 \begin {gather*} \frac {x (f x)^m \left (b n (1+m-r) \left (d+e x^r\right ) \, _3F_2\left (1,\frac {1}{r}+\frac {m}{r},\frac {1}{r}+\frac {m}{r};1+\frac {1}{r}+\frac {m}{r},1+\frac {1}{r}+\frac {m}{r};-\frac {e x^r}{d}\right )-(1+m) \left (-d (1+m) \left (a+b \log \left (c x^n\right )\right )+\left (d+e x^r\right ) \, _2F_1\left (1,\frac {1+m}{r};\frac {1+m+r}{r};-\frac {e x^r}{d}\right ) \left (b n+a (1+m-r)+b (1+m-r) \log \left (c x^n\right )\right )\right )\right )}{d^2 (1+m)^2 r \left (d+e x^r\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.05, size = 0, normalized size = 0.00 \[\int \frac {\left (f x \right )^{m} \left (a +b \ln \left (c \,x^{n}\right )\right )}{\left (d +e \,x^{r}\right )^{2}}\, dx\]
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 {\left (f x\right )^{m} \left (a + b \log {\left (c x^{n} \right )}\right )}{\left (d + e x^{r}\right )^{2}}\, 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 {{\left (f\,x\right )}^m\,\left (a+b\,\ln \left (c\,x^n\right )\right )}{{\left (d+e\,x^r\right )}^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________