Optimal. Leaf size=9 \[ \frac{\sin (x)}{\cos (x)+1} \]
[Out]
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Rubi [A] time = 0.0176253, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ \frac{\sin (x)}{\cos (x)+1} \]
Antiderivative was successfully verified.
[In] Int[(1 + Cos[x])^(-1),x]
[Out]
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Rubi in Sympy [A] time = 0.486752, size = 7, normalized size = 0.78 \[ \frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1+cos(x)),x)
[Out]
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Mathematica [A] time = 0.00601184, size = 6, normalized size = 0.67 \[ \tan \left (\frac{x}{2}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(1 + Cos[x])^(-1),x]
[Out]
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Maple [A] time = 0.002, size = 5, normalized size = 0.6 \[ \tan \left ({\frac{x}{2}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1+cos(x)),x)
[Out]
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Maxima [A] time = 1.34632, size = 12, normalized size = 1.33 \[ \frac{\sin \left (x\right )}{\cos \left (x\right ) + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(cos(x) + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217694, size = 12, normalized size = 1.33 \[ \frac{\sin \left (x\right )}{\cos \left (x\right ) + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(cos(x) + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.210411, size = 3, normalized size = 0.33 \[ \tan{\left (\frac{x}{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1+cos(x)),x)
[Out]
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GIAC/XCAS [A] time = 0.206472, size = 41, normalized size = 4.56 \[ -\frac{2 \, \tan \left (\frac{1}{2} \, x\right )}{{\left (x^{2} + 1\right )}{\left (\frac{x^{2} - 1}{x^{2} + 1} - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(cos(x) + 1),x, algorithm="giac")
[Out]