Optimal. Leaf size=24 \[ \frac {1}{2} b^4 f^a \log ^4(f) \Gamma \left (-4,-\frac {b \log (f)}{x^2}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 1.00, 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} \[ \frac {1}{2} b^4 f^a \log ^4(f) \text {Gamma}\left (-4,-\frac {b \log (f)}{x^2}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2218
Rubi steps
\begin {align*} \int f^{a+\frac {b}{x^2}} x^7 \, dx &=\frac {1}{2} b^4 f^a \Gamma \left (-4,-\frac {b \log (f)}{x^2}\right ) \log ^4(f)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 24, normalized size = 1.00 \[ \frac {1}{2} b^4 f^a \log ^4(f) \Gamma \left (-4,-\frac {b \log (f)}{x^2}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.42, size = 72, normalized size = 3.00 \[ -\frac {1}{48} \, b^{4} f^{a} {\rm Ei}\left (\frac {b \log \relax (f)}{x^{2}}\right ) \log \relax (f)^{4} + \frac {1}{48} \, {\left (6 \, x^{8} + 2 \, b x^{6} \log \relax (f) + b^{2} x^{4} \log \relax (f)^{2} + b^{3} x^{2} \log \relax (f)^{3}\right )} f^{\frac {a x^{2} + b}{x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int f^{a + \frac {b}{x^{2}}} x^{7}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.07, size = 101, normalized size = 4.21 \[ \frac {b^{4} f^{a} \Ei \left (1, -\frac {b \ln \relax (f )}{x^{2}}\right ) \ln \relax (f )^{4}}{48}+\frac {b^{3} x^{2} f^{a} f^{\frac {b}{x^{2}}} \ln \relax (f )^{3}}{48}+\frac {b^{2} x^{4} f^{a} f^{\frac {b}{x^{2}}} \ln \relax (f )^{2}}{48}+\frac {b \,x^{6} f^{a} f^{\frac {b}{x^{2}}} \ln \relax (f )}{24}+\frac {x^{8} f^{a} f^{\frac {b}{x^{2}}}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 1.35, size = 22, normalized size = 0.92 \[ \frac {1}{2} \, b^{4} f^{a} \Gamma \left (-4, -\frac {b \log \relax (f)}{x^{2}}\right ) \log \relax (f)^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.77, size = 90, normalized size = 3.75 \[ \frac {b^4\,f^a\,{\ln \relax (f)}^4\,\mathrm {expint}\left (-\frac {b\,\ln \relax (f)}{x^2}\right )}{48}+\frac {b^4\,f^a\,f^{\frac {b}{x^2}}\,{\ln \relax (f)}^4\,\left (\frac {x^2}{24\,b\,\ln \relax (f)}+\frac {x^4}{24\,b^2\,{\ln \relax (f)}^2}+\frac {x^6}{12\,b^3\,{\ln \relax (f)}^3}+\frac {x^8}{4\,b^4\,{\ln \relax (f)}^4}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int f^{a + \frac {b}{x^{2}}} x^{7}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________