Optimal. Leaf size=34 \[ \frac{5 x}{16}+\frac{1}{6} \sin (x) \cos ^5(x)+\frac{5}{24} \sin (x) \cos ^3(x)+\frac{5}{16} \sin (x) \cos (x) \]
[Out]
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Rubi [A] time = 0.0285844, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ \frac{5 x}{16}+\frac{1}{6} \sin (x) \cos ^5(x)+\frac{5}{24} \sin (x) \cos ^3(x)+\frac{5}{16} \sin (x) \cos (x) \]
Antiderivative was successfully verified.
[In] Int[Cos[x]^6,x]
[Out]
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Rubi in Sympy [A] time = 0.67649, size = 36, normalized size = 1.06 \[ \frac{5 x}{16} + \frac{\sin{\left (x \right )} \cos ^{5}{\left (x \right )}}{6} + \frac{5 \sin{\left (x \right )} \cos ^{3}{\left (x \right )}}{24} + \frac{5 \sin{\left (x \right )} \cos{\left (x \right )}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)**6,x)
[Out]
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Mathematica [A] time = 0.0034475, size = 30, normalized size = 0.88 \[ \frac{5 x}{16}+\frac{15}{64} \sin (2 x)+\frac{3}{64} \sin (4 x)+\frac{1}{192} \sin (6 x) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]^6,x]
[Out]
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Maple [A] time = 0.056, size = 24, normalized size = 0.7 \[{\frac{\sin \left ( x \right ) }{6} \left ( \left ( \cos \left ( x \right ) \right ) ^{5}+{\frac{5\, \left ( \cos \left ( x \right ) \right ) ^{3}}{4}}+{\frac{15\,\cos \left ( x \right ) }{8}} \right ) }+{\frac{5\,x}{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)^6,x)
[Out]
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Maxima [A] time = 1.5101, size = 32, normalized size = 0.94 \[ -\frac{1}{48} \, \sin \left (2 \, x\right )^{3} + \frac{5}{16} \, x + \frac{3}{64} \, \sin \left (4 \, x\right ) + \frac{1}{4} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.246802, size = 34, normalized size = 1. \[ \frac{1}{48} \,{\left (8 \, \cos \left (x\right )^{5} + 10 \, \cos \left (x\right )^{3} + 15 \, \cos \left (x\right )\right )} \sin \left (x\right ) + \frac{5}{16} \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.038221, size = 36, normalized size = 1.06 \[ \frac{5 x}{16} + \frac{\sin{\left (x \right )} \cos ^{5}{\left (x \right )}}{6} + \frac{5 \sin{\left (x \right )} \cos ^{3}{\left (x \right )}}{24} + \frac{5 \sin{\left (x \right )} \cos{\left (x \right )}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)**6,x)
[Out]
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GIAC/XCAS [A] time = 0.200061, size = 30, normalized size = 0.88 \[ \frac{5}{16} \, x + \frac{1}{192} \, \sin \left (6 \, x\right ) + \frac{3}{64} \, \sin \left (4 \, x\right ) + \frac{15}{64} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^6,x, algorithm="giac")
[Out]