Optimal. Leaf size=15 \[ \frac {1}{2} f^a \text {Ei}\left (b x^2 \log (f)\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 15, 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 = {2241}
\begin {gather*} \frac {1}{2} f^a \text {Ei}\left (b x^2 \log (f)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2241
Rubi steps
\begin {align*} \int \frac {f^{a+b x^2}}{x} \, dx &=\frac {1}{2} f^a \text {Ei}\left (b x^2 \log (f)\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 15, normalized size = 1.00 \begin {gather*} \frac {1}{2} f^a \text {Ei}\left (b x^2 \log (f)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 16, normalized size = 1.07
method | result | size |
risch | \(-\frac {f^{a} \expIntegral \left (1, -b \,x^{2} \ln \left (f \right )\right )}{2}\) | \(16\) |
meijerg | \(\frac {f^{a} \left (-\ln \left (-b \,x^{2} \ln \left (f \right )\right )-\expIntegral \left (1, -b \,x^{2} \ln \left (f \right )\right )+2 \ln \left (x \right )+\ln \left (-b \right )+\ln \left (\ln \left (f \right )\right )\right )}{2}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.32, size = 13, normalized size = 0.87 \begin {gather*} \frac {1}{2} \, f^{a} {\rm Ei}\left (b x^{2} \log \left (f\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.42, size = 13, normalized size = 0.87 \begin {gather*} \frac {1}{2} \, f^{a} {\rm Ei}\left (b x^{2} \log \left (f\right )\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 + b x^{2}}}{x}\, 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 = 3.18, size = 13, normalized size = 0.87 \begin {gather*} \frac {f^a\,\mathrm {ei}\left (b\,x^2\,\ln \left (f\right )\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________