Optimal. Leaf size=24 \[ \frac{3 x}{8}+\frac{1}{4} \sin (x) \cos ^3(x)+\frac{3}{8} \sin (x) \cos (x) \]
[Out]
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Rubi [A] time = 0.0185558, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ \frac{3 x}{8}+\frac{1}{4} \sin (x) \cos ^3(x)+\frac{3}{8} \sin (x) \cos (x) \]
Antiderivative was successfully verified.
[In] Int[Cos[x]^4,x]
[Out]
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Rubi in Sympy [A] time = 0.59117, size = 24, normalized size = 1. \[ \frac{3 x}{8} + \frac{\sin{\left (x \right )} \cos ^{3}{\left (x \right )}}{4} + \frac{3 \sin{\left (x \right )} \cos{\left (x \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)**4,x)
[Out]
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Mathematica [A] time = 0.00288593, size = 22, normalized size = 0.92 \[ \frac{3 x}{8}+\frac{1}{4} \sin (2 x)+\frac{1}{32} \sin (4 x) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]^4,x]
[Out]
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Maple [A] time = 0.062, size = 18, normalized size = 0.8 \[{\frac{\sin \left ( x \right ) }{4} \left ( \left ( \cos \left ( x \right ) \right ) ^{3}+{\frac{3\,\cos \left ( x \right ) }{2}} \right ) }+{\frac{3\,x}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)^4,x)
[Out]
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Maxima [A] time = 1.35768, size = 22, normalized size = 0.92 \[ \frac{3}{8} \, x + \frac{1}{32} \, \sin \left (4 \, x\right ) + \frac{1}{4} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.246385, size = 26, normalized size = 1.08 \[ \frac{1}{8} \,{\left (2 \, \cos \left (x\right )^{3} + 3 \, \cos \left (x\right )\right )} \sin \left (x\right ) + \frac{3}{8} \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.03856, size = 24, normalized size = 1. \[ \frac{3 x}{8} + \frac{\sin{\left (x \right )} \cos ^{3}{\left (x \right )}}{4} + \frac{3 \sin{\left (x \right )} \cos{\left (x \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.236757, size = 22, normalized size = 0.92 \[ \frac{3}{8} \, x + \frac{1}{32} \, \sin \left (4 \, x\right ) + \frac{1}{4} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^4,x, algorithm="giac")
[Out]