Optimal. Leaf size=34 \[ \frac {f^a \Gamma \left (\frac {2}{3},-\frac {b \log (f)}{x^3}\right )}{3 x^2 \left (-\frac {b \log (f)}{x^3}\right )^{2/3}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 34, 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 = {2250}
\begin {gather*} \frac {f^a \text {Gamma}\left (\frac {2}{3},-\frac {b \log (f)}{x^3}\right )}{3 x^2 \left (-\frac {b \log (f)}{x^3}\right )^{2/3}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2250
Rubi steps
\begin {align*} \int \frac {f^{a+\frac {b}{x^3}}}{x^3} \, dx &=\frac {f^a \Gamma \left (\frac {2}{3},-\frac {b \log (f)}{x^3}\right )}{3 x^2 \left (-\frac {b \log (f)}{x^3}\right )^{2/3}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 34, normalized size = 1.00 \begin {gather*} \frac {f^a \Gamma \left (\frac {2}{3},-\frac {b \log (f)}{x^3}\right )}{3 x^2 \left (-\frac {b \log (f)}{x^3}\right )^{2/3}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(77\) vs.
\(2(28)=56\).
time = 0.03, size = 78, normalized size = 2.29
method | result | size |
meijerg | \(\frac {f^{a} \left (-b \right )^{\frac {1}{3}} \left (\frac {\left (-b \right )^{\frac {2}{3}} \ln \left (f \right )^{\frac {2}{3}} \Gamma \left (\frac {2}{3}\right )}{x^{2} \left (-\frac {b \ln \left (f \right )}{x^{3}}\right )^{\frac {2}{3}}}-\frac {\left (-b \right )^{\frac {2}{3}} \ln \left (f \right )^{\frac {2}{3}} \Gamma \left (\frac {2}{3}, -\frac {b \ln \left (f \right )}{x^{3}}\right )}{x^{2} \left (-\frac {b \ln \left (f \right )}{x^{3}}\right )^{\frac {2}{3}}}\right )}{3 b \ln \left (f \right )^{\frac {2}{3}}}\) | \(78\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.06, size = 28, normalized size = 0.82 \begin {gather*} \frac {f^{a} \Gamma \left (\frac {2}{3}, -\frac {b \log \left (f\right )}{x^{3}}\right )}{3 \, x^{2} \left (-\frac {b \log \left (f\right )}{x^{3}}\right )^{\frac {2}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.08, size = 29, normalized size = 0.85 \begin {gather*} -\frac {\left (-b \log \left (f\right )\right )^{\frac {1}{3}} f^{a} \Gamma \left (\frac {2}{3}, -\frac {b \log \left (f\right )}{x^{3}}\right )}{3 \, b \log \left (f\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {f^{a + \frac {b}{x^{3}}}}{x^{3}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
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 [B]
time = 3.56, size = 33, normalized size = 0.97 \begin {gather*} -\frac {f^a\,\left (\Gamma \left (\frac {2}{3}\right )-\Gamma \left (\frac {2}{3},-\frac {b\,\ln \left (f\right )}{x^3}\right )\right )}{3\,x^2\,{\left (-\frac {b\,\ln \left (f\right )}{x^3}\right )}^{2/3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________