Optimal. Leaf size=15 \[ \frac {f^a \text {Ei}\left (b x^n \log (f)\right )}{n} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, 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 = {2210} \[ \frac {f^a \text {Ei}\left (b x^n \log (f)\right )}{n} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2210
Rubi steps
\begin {align*} \int \frac {f^{a+b x^n}}{x} \, dx &=\frac {f^a \text {Ei}\left (b x^n \log (f)\right )}{n}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ \frac {f^a \text {Ei}\left (b x^n \log (f)\right )}{n} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.41, size = 15, normalized size = 1.00 \[ \frac {f^{a} {\rm Ei}\left (b x^{n} \log \relax (f)\right )}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {f^{b x^{n} + a}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.21, size = 19, normalized size = 1.27 \[ -\frac {f^{a} \Ei \left (1, -b \,x^{n} \ln \relax (f )\right )}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.94, size = 15, normalized size = 1.00 \[ \frac {f^{a} {\rm Ei}\left (b x^{n} \log \relax (f)\right )}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {f^{a+b\,x^n}}{x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {f^{a + b x^{n}}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________