Optimal. Leaf size=20 \[ \frac{f^{a+b x^2}}{2 b \log (f)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.023673, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{f^{a+b x^2}}{2 b \log (f)} \]
Antiderivative was successfully verified.
[In] Int[f^(a + b*x^2)*x,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.55136, size = 14, normalized size = 0.7 \[ \frac{f^{a + b x^{2}}}{2 b \log{\left (f \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(b*x**2+a)*x,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00388811, size = 20, normalized size = 1. \[ \frac{f^{a+b x^2}}{2 b \log (f)} \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b*x^2)*x,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 19, normalized size = 1. \[{\frac{{f}^{b{x}^{2}+a}}{2\,b\ln \left ( f \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(b*x^2+a)*x,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.762497, size = 24, normalized size = 1.2 \[ \frac{f^{b x^{2} + a}}{2 \, b \log \left (f\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^2 + a)*x,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.236463, size = 24, normalized size = 1.2 \[ \frac{f^{b x^{2} + a}}{2 \, b \log \left (f\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^2 + a)*x,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.18018, size = 24, normalized size = 1.2 \[ \begin{cases} \frac{f^{a + b x^{2}}}{2 b \log{\left (f \right )}} & \text{for}\: 2 b \log{\left (f \right )} \neq 0 \\\frac{x^{2}}{2} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(b*x**2+a)*x,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.229338, size = 24, normalized size = 1.2 \[ \frac{f^{b x^{2} + a}}{2 \, b{\rm ln}\left (f\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^2 + a)*x,x, algorithm="giac")
[Out]