Optimal. Leaf size=8 \[ \frac{\sec ^2(x)}{2} \]
[Out]
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Rubi [A] time = 0.0197046, 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]
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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/cot(x),x)
[Out]
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Mathematica [A] time = 0.00268946, size = 8, normalized size = 1. \[ \frac{\sec ^2(x)}{2} \]
Antiderivative was successfully verified.
[In] Integrate[Sec[x]^2*Tan[x],x]
[Out]
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Maple [A] time = 0.018, 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/cot(x),x)
[Out]
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Maxima [A] time = 1.37236, size = 14, normalized size = 1.75 \[ -\frac{1}{2 \,{\left (\sin \left (x\right )^{2} - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^2/cot(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212081, 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/cot(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.057229, 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/cot(x),x)
[Out]
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GIAC/XCAS [A] time = 0.20019, 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/cot(x),x, algorithm="giac")
[Out]