Optimal. Leaf size=24 \[ \frac{1}{2} b^5 f^a \log ^5(f) \text{Gamma}\left (-5,-b x^2 \log (f)\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0228089, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {2218} \[ \frac{1}{2} b^5 f^a \log ^5(f) \text{Gamma}\left (-5,-b x^2 \log (f)\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2218
Rubi steps
\begin{align*} \int \frac{f^{a+b x^2}}{x^{11}} \, dx &=\frac{1}{2} b^5 f^a \Gamma \left (-5,-b x^2 \log (f)\right ) \log ^5(f)\\ \end{align*}
Mathematica [A] time = 0.0024617, size = 24, normalized size = 1. \[ \frac{1}{2} b^5 f^a \log ^5(f) \text{Gamma}\left (-5,-b x^2 \log (f)\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] time = 0.066, size = 123, normalized size = 5.1 \begin{align*} -{\frac{{f}^{a}{f}^{b{x}^{2}}}{10\,{x}^{10}}}-{\frac{{f}^{a}\ln \left ( f \right ) b{f}^{b{x}^{2}}}{40\,{x}^{8}}}-{\frac{{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}{f}^{b{x}^{2}}}{120\,{x}^{6}}}-{\frac{{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}{f}^{b{x}^{2}}}{240\,{x}^{4}}}-{\frac{{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{4}{b}^{4}{f}^{b{x}^{2}}}{240\,{x}^{2}}}-{\frac{{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{5}{b}^{5}{\it Ei} \left ( 1,-b{x}^{2}\ln \left ( f \right ) \right ) }{240}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{f^{a + b x^{2}}}{x^{11}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{f^{b x^{2} + a}}{x^{11}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]