Optimal. Leaf size=21 \[ -\frac{1}{5} \cos ^5(x)+\frac{2 \cos ^3(x)}{3}-\cos (x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0126419, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ -\frac{1}{5} \cos ^5(x)+\frac{2 \cos ^3(x)}{3}-\cos (x) \]
Antiderivative was successfully verified.
[In] Int[Sin[x]^5,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 0.744482, size = 17, normalized size = 0.81 \[ - \frac{\cos ^{5}{\left (x \right )}}{5} + \frac{2 \cos ^{3}{\left (x \right )}}{3} - \cos{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(sin(x)**5,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00320367, size = 23, normalized size = 1.1 \[ -\frac{5 \cos (x)}{8}+\frac{5}{48} \cos (3 x)-\frac{1}{80} \cos (5 x) \]
Antiderivative was successfully verified.
[In] Integrate[Sin[x]^5,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.053, size = 17, normalized size = 0.8 \[ -{\frac{\cos \left ( x \right ) }{5} \left ({\frac{8}{3}}+ \left ( \sin \left ( x \right ) \right ) ^{4}+{\frac{4\, \left ( \sin \left ( x \right ) \right ) ^{2}}{3}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(sin(x)^5,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.48142, size = 23, normalized size = 1.1 \[ -\frac{1}{5} \, \cos \left (x\right )^{5} + \frac{2}{3} \, \cos \left (x\right )^{3} - \cos \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)^5,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.216444, size = 23, normalized size = 1.1 \[ -\frac{1}{5} \, \cos \left (x\right )^{5} + \frac{2}{3} \, \cos \left (x\right )^{3} - \cos \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)^5,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.046102, size = 17, normalized size = 0.81 \[ - \frac{\cos ^{5}{\left (x \right )}}{5} + \frac{2 \cos ^{3}{\left (x \right )}}{3} - \cos{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)**5,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.223361, size = 23, normalized size = 1.1 \[ -\frac{1}{5} \, \cos \left (x\right )^{5} + \frac{2}{3} \, \cos \left (x\right )^{3} - \cos \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)^5,x, algorithm="giac")
[Out]