Optimal. Leaf size=46 \[ \frac{3 x}{128}-\frac{1}{8} \sin ^3(x) \cos ^5(x)-\frac{1}{16} \sin (x) \cos ^5(x)+\frac{1}{64} \sin (x) \cos ^3(x)+\frac{3}{128} \sin (x) \cos (x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.08663, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 3, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ \frac{3 x}{128}-\frac{1}{8} \sin ^3(x) \cos ^5(x)-\frac{1}{16} \sin (x) \cos ^5(x)+\frac{1}{64} \sin (x) \cos ^3(x)+\frac{3}{128} \sin (x) \cos (x) \]
Antiderivative was successfully verified.
[In] Int[Cos[x]^4*Sin[x]^4,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.98813, size = 46, normalized size = 1. \[ \frac{3 x}{128} - \frac{\sin ^{3}{\left (x \right )} \cos ^{5}{\left (x \right )}}{8} - \frac{\sin{\left (x \right )} \cos ^{5}{\left (x \right )}}{16} + \frac{\sin{\left (x \right )} \cos ^{3}{\left (x \right )}}{64} + \frac{3 \sin{\left (x \right )} \cos{\left (x \right )}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)**4*sin(x)**4,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00957197, size = 22, normalized size = 0.48 \[ \frac{3 x}{128}-\frac{1}{128} \sin (4 x)+\frac{\sin (8 x)}{1024} \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]^4*Sin[x]^4,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 36, normalized size = 0.8 \[ -{\frac{ \left ( \cos \left ( x \right ) \right ) ^{5} \left ( \sin \left ( x \right ) \right ) ^{3}}{8}}-{\frac{ \left ( \cos \left ( x \right ) \right ) ^{5}\sin \left ( x \right ) }{16}}+{\frac{\sin \left ( x \right ) }{64} \left ( \left ( \cos \left ( x \right ) \right ) ^{3}+{\frac{3\,\cos \left ( x \right ) }{2}} \right ) }+{\frac{3\,x}{128}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)^4*sin(x)^4,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43621, size = 22, normalized size = 0.48 \[ \frac{3}{128} \, x + \frac{1}{1024} \, \sin \left (8 \, x\right ) - \frac{1}{128} \, \sin \left (4 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^4*sin(x)^4,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.217911, size = 42, normalized size = 0.91 \[ \frac{1}{128} \,{\left (16 \, \cos \left (x\right )^{7} - 24 \, \cos \left (x\right )^{5} + 2 \, \cos \left (x\right )^{3} + 3 \, \cos \left (x\right )\right )} \sin \left (x\right ) + \frac{3}{128} \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^4*sin(x)^4,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.053401, size = 31, normalized size = 0.67 \[ \frac{3 x}{128} - \frac{\sin ^{3}{\left (2 x \right )} \cos{\left (2 x \right )}}{128} - \frac{3 \sin{\left (2 x \right )} \cos{\left (2 x \right )}}{256} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)**4*sin(x)**4,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.197948, size = 22, normalized size = 0.48 \[ \frac{3}{128} \, x + \frac{1}{1024} \, \sin \left (8 \, x\right ) - \frac{1}{128} \, \sin \left (4 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^4*sin(x)^4,x, algorithm="giac")
[Out]