Optimal. Leaf size=14 \[ \frac{x}{2}+\frac{1}{2} \sin (x) \cos (x) \]
[Out]
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Rubi [A] time = 0.0107597, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ \frac{x}{2}+\frac{1}{2} \sin (x) \cos (x) \]
Antiderivative was successfully verified.
[In] Int[Cos[x]^2,x]
[Out]
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Rubi in Sympy [A] time = 0.493882, size = 10, normalized size = 0.71 \[ \frac{x}{2} + \frac{\sin{\left (x \right )} \cos{\left (x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/sec(x)**2,x)
[Out]
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Mathematica [A] time = 0.00290481, size = 14, normalized size = 1. \[ \frac{x}{2}+\frac{1}{4} \sin (2 x) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]^2,x]
[Out]
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Maple [A] time = 0.006, size = 11, normalized size = 0.8 \[{\frac{x}{2}}+{\frac{\cos \left ( x \right ) \sin \left ( x \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/sec(x)^2,x)
[Out]
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Maxima [A] time = 1.40299, size = 14, normalized size = 1. \[ \frac{1}{2} \, x + \frac{1}{4} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^(-2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228423, size = 14, normalized size = 1. \[ \frac{1}{2} \, \cos \left (x\right ) \sin \left (x\right ) + \frac{1}{2} \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^(-2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.05551, size = 10, normalized size = 0.71 \[ \frac{x}{2} + \frac{\sin{\left (x \right )} \cos{\left (x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sec(x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.203797, size = 22, normalized size = 1.57 \[ \frac{1}{2} \, x + \frac{\tan \left (x\right )}{2 \,{\left (\tan \left (x\right )^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sec(x)^(-2),x, algorithm="giac")
[Out]