Optimal. Leaf size=34 \[ \frac{x}{16}-\frac{1}{6} \sin (x) \cos ^5(x)+\frac{1}{24} \sin (x) \cos ^3(x)+\frac{1}{16} \sin (x) \cos (x) \]
[Out]
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Rubi [A] time = 0.0516699, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ \frac{x}{16}-\frac{1}{6} \sin (x) \cos ^5(x)+\frac{1}{24} \sin (x) \cos ^3(x)+\frac{1}{16} \sin (x) \cos (x) \]
Antiderivative was successfully verified.
[In] Int[Cos[x]^4*Sin[x]^2,x]
[Out]
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Rubi in Sympy [A] time = 1.70566, size = 31, normalized size = 0.91 \[ \frac{x}{16} - \frac{\sin{\left (x \right )} \cos ^{5}{\left (x \right )}}{6} + \frac{\sin{\left (x \right )} \cos ^{3}{\left (x \right )}}{24} + \frac{\sin{\left (x \right )} \cos{\left (x \right )}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)**4*sin(x)**2,x)
[Out]
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Mathematica [A] time = 0.0126713, size = 30, normalized size = 0.88 \[ \frac{x}{16}+\frac{1}{64} \sin (2 x)-\frac{1}{64} \sin (4 x)-\frac{1}{192} \sin (6 x) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]^4*Sin[x]^2,x]
[Out]
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Maple [A] time = 0.003, size = 26, normalized size = 0.8 \[ -{\frac{ \left ( \cos \left ( x \right ) \right ) ^{5}\sin \left ( x \right ) }{6}}+{\frac{\sin \left ( x \right ) }{24} \left ( \left ( \cos \left ( x \right ) \right ) ^{3}+{\frac{3\,\cos \left ( x \right ) }{2}} \right ) }+{\frac{x}{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)^4*sin(x)^2,x)
[Out]
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Maxima [A] time = 1.34326, size = 24, normalized size = 0.71 \[ \frac{1}{48} \, \sin \left (2 \, x\right )^{3} + \frac{1}{16} \, x - \frac{1}{64} \, \sin \left (4 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^4*sin(x)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237579, size = 34, normalized size = 1. \[ -\frac{1}{48} \,{\left (8 \, \cos \left (x\right )^{5} - 2 \, \cos \left (x\right )^{3} - 3 \, \cos \left (x\right )\right )} \sin \left (x\right ) + \frac{1}{16} \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^4*sin(x)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.054746, size = 31, normalized size = 0.91 \[ \frac{x}{16} - \frac{\sin{\left (x \right )} \cos ^{5}{\left (x \right )}}{6} + \frac{\sin{\left (x \right )} \cos ^{3}{\left (x \right )}}{24} + \frac{\sin{\left (x \right )} \cos{\left (x \right )}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)**4*sin(x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.227424, size = 30, normalized size = 0.88 \[ \frac{1}{16} \, x - \frac{1}{192} \, \sin \left (6 \, x\right ) - \frac{1}{64} \, \sin \left (4 \, x\right ) + \frac{1}{64} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^4*sin(x)^2,x, algorithm="giac")
[Out]