Optimal. Leaf size=82 \[ \frac{f^{a+\frac{b}{x^3}} \left (60 b^2 x^9 \log ^2(f)-20 b^3 x^6 \log ^3(f)+5 b^4 x^3 \log ^4(f)-b^5 \log ^5(f)-120 b x^{12} \log (f)+120 x^{15}\right )}{3 b^6 x^{15} \log ^6(f)} \]
[Out]
________________________________________________________________________________________
Rubi [C] time = 0.0228049, antiderivative size = 24, normalized size of antiderivative = 0.29, 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} \[ \frac{f^a \text{Gamma}\left (6,-\frac{b \log (f)}{x^3}\right )}{3 b^6 \log ^6(f)} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2218
Rubi steps
\begin{align*} \int \frac{f^{a+\frac{b}{x^3}}}{x^{19}} \, dx &=\frac{f^a \Gamma \left (6,-\frac{b \log (f)}{x^3}\right )}{3 b^6 \log ^6(f)}\\ \end{align*}
Mathematica [C] time = 0.0029883, size = 24, normalized size = 0.29 \[ \frac{f^a \text{Gamma}\left (6,-\frac{b \log (f)}{x^3}\right )}{3 b^6 \log ^6(f)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.029, size = 84, normalized size = 1. \begin{align*} -{\frac{-120\,{x}^{15}+120\,b{x}^{12}\ln \left ( f \right ) -60\,{b}^{2}{x}^{9} \left ( \ln \left ( f \right ) \right ) ^{2}+20\,{b}^{3}{x}^{6} \left ( \ln \left ( f \right ) \right ) ^{3}-5\,{b}^{4}{x}^{3} \left ( \ln \left ( f \right ) \right ) ^{4}+{b}^{5} \left ( \ln \left ( f \right ) \right ) ^{5}}{3\, \left ( \ln \left ( f \right ) \right ) ^{6}{b}^{6}{x}^{15}}{f}^{{\frac{a{x}^{3}+b}{{x}^{3}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [C] time = 1.18733, size = 30, normalized size = 0.37 \begin{align*} \frac{f^{a} \Gamma \left (6, -\frac{b \log \left (f\right )}{x^{3}}\right )}{3 \, b^{6} \log \left (f\right )^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.01496, size = 211, normalized size = 2.57 \begin{align*} \frac{{\left (120 \, x^{15} - 120 \, b x^{12} \log \left (f\right ) + 60 \, b^{2} x^{9} \log \left (f\right )^{2} - 20 \, b^{3} x^{6} \log \left (f\right )^{3} + 5 \, b^{4} x^{3} \log \left (f\right )^{4} - b^{5} \log \left (f\right )^{5}\right )} f^{\frac{a x^{3} + b}{x^{3}}}}{3 \, b^{6} x^{15} \log \left (f\right )^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.161392, size = 85, normalized size = 1.04 \begin{align*} \frac{f^{a + \frac{b}{x^{3}}} \left (- b^{5} \log{\left (f \right )}^{5} + 5 b^{4} x^{3} \log{\left (f \right )}^{4} - 20 b^{3} x^{6} \log{\left (f \right )}^{3} + 60 b^{2} x^{9} \log{\left (f \right )}^{2} - 120 b x^{12} \log{\left (f \right )} + 120 x^{15}\right )}{3 b^{6} x^{15} \log{\left (f \right )}^{6}} \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^{a + \frac{b}{x^{3}}}}{x^{19}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]