Optimal. Leaf size=8 \[ \frac{\sec ^2(x)}{2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.017114, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ \frac{\sec ^2(x)}{2} \]
Antiderivative was successfully verified.
[In] Int[Sec[x]^2*Tan[x],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int ^{\tan{\left (x \right )}} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(sec(x)**2*tan(x),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0030232, size = 8, normalized size = 1. \[ \frac{\sec ^2(x)}{2} \]
Antiderivative was successfully verified.
[In] Integrate[Sec[x]^2*Tan[x],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 7, normalized size = 0.9 \[{\frac{ \left ( \sec \left ( x \right ) \right ) ^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(sec(x)^2*tan(x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.32574, size = 8, normalized size = 1. \[ \frac{1}{2} \, \tan \left (x\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^2*tan(x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.224094, size = 8, normalized size = 1. \[ \frac{1}{2 \, \cos \left (x\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^2*tan(x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.050914, size = 7, normalized size = 0.88 \[ \frac{1}{2 \cos ^{2}{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)**2*tan(x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.198484, size = 8, normalized size = 1. \[ \frac{1}{2 \, \cos \left (x\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^2*tan(x),x, algorithm="giac")
[Out]