Optimal. Leaf size=24 \[ \frac{x}{8}-\frac{1}{4} \sin (x) \cos ^3(x)+\frac{1}{8} \sin (x) \cos (x) \]
[Out]
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Rubi [A] time = 0.0387615, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ \frac{x}{8}-\frac{1}{4} \sin (x) \cos ^3(x)+\frac{1}{8} \sin (x) \cos (x) \]
Antiderivative was successfully verified.
[In] Int[Cos[x]^2*Sin[x]^2,x]
[Out]
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Rubi in Sympy [A] time = 1.62506, size = 20, normalized size = 0.83 \[ \frac{x}{8} - \frac{\sin{\left (x \right )} \cos ^{3}{\left (x \right )}}{4} + \frac{\sin{\left (x \right )} \cos{\left (x \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)**2*sin(x)**2,x)
[Out]
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Mathematica [A] time = 0.00647966, size = 14, normalized size = 0.58 \[ \frac{x}{8}-\frac{1}{32} \sin (4 x) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]^2*Sin[x]^2,x]
[Out]
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Maple [A] time = 0.002, size = 19, normalized size = 0.8 \[{\frac{x}{8}}+{\frac{\cos \left ( x \right ) \sin \left ( x \right ) }{8}}-{\frac{ \left ( \cos \left ( x \right ) \right ) ^{3}\sin \left ( x \right ) }{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)^2*sin(x)^2,x)
[Out]
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Maxima [A] time = 1.34772, size = 14, normalized size = 0.58 \[ \frac{1}{8} \, x - \frac{1}{32} \, \sin \left (4 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^2*sin(x)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221972, size = 26, normalized size = 1.08 \[ -\frac{1}{8} \,{\left (2 \, \cos \left (x\right )^{3} - \cos \left (x\right )\right )} \sin \left (x\right ) + \frac{1}{8} \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^2*sin(x)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.052749, size = 14, normalized size = 0.58 \[ \frac{x}{8} - \frac{\sin{\left (2 x \right )} \cos{\left (2 x \right )}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)**2*sin(x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.219669, size = 14, normalized size = 0.58 \[ \frac{1}{8} \, x - \frac{1}{32} \, \sin \left (4 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^2*sin(x)^2,x, algorithm="giac")
[Out]