Optimal. Leaf size=20 \[ \frac {f^{a+b x^3}}{3 b \log (f)} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 20, 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 = {2209} \[ \frac {f^{a+b x^3}}{3 b \log (f)} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2209
Rubi steps
\begin {align*} \int f^{a+b x^3} x^2 \, dx &=\frac {f^{a+b x^3}}{3 b \log (f)}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 20, normalized size = 1.00 \[ \frac {f^{a+b x^3}}{3 b \log (f)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.44, size = 18, normalized size = 0.90 \[ \frac {f^{b x^{3} + a}}{3 \, b \log \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.21, size = 18, normalized size = 0.90 \[ \frac {f^{b x^{3} + a}}{3 \, b \log \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 19, normalized size = 0.95 \[ \frac {f^{b \,x^{3}+a}}{3 b \ln \relax (f )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.93, size = 18, normalized size = 0.90 \[ \frac {f^{b x^{3} + a}}{3 \, b \log \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.47, size = 18, normalized size = 0.90 \[ \frac {f^{b\,x^3+a}}{3\,b\,\ln \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 24, normalized size = 1.20 \[ \begin {cases} \frac {f^{a + b x^{3}}}{3 b \log {\relax (f )}} & \text {for}\: 3 b \log {\relax (f )} \neq 0 \\\frac {x^{3}}{3} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________