Optimal. Leaf size=25 \[ -\frac{1}{7} \cos ^7(x)+\frac{2 \cos ^5(x)}{5}-\frac{\cos ^3(x)}{3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0467748, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ -\frac{1}{7} \cos ^7(x)+\frac{2 \cos ^5(x)}{5}-\frac{\cos ^3(x)}{3} \]
Antiderivative was successfully verified.
[In] Int[Cos[x]^2*Sin[x]^5,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.10453, size = 20, normalized size = 0.8 \[ - \frac{\cos ^{7}{\left (x \right )}}{7} + \frac{2 \cos ^{5}{\left (x \right )}}{5} - \frac{\cos ^{3}{\left (x \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)**2*sin(x)**5,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0166215, size = 31, normalized size = 1.24 \[ -\frac{5 \cos (x)}{64}-\frac{1}{192} \cos (3 x)+\frac{3}{320} \cos (5 x)-\frac{1}{448} \cos (7 x) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]^2*Sin[x]^5,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.016, size = 28, normalized size = 1.1 \[ -{\frac{ \left ( \cos \left ( x \right ) \right ) ^{3} \left ( \sin \left ( x \right ) \right ) ^{4}}{7}}-{\frac{4\, \left ( \sin \left ( x \right ) \right ) ^{2} \left ( \cos \left ( x \right ) \right ) ^{3}}{35}}-{\frac{8\, \left ( \cos \left ( x \right ) \right ) ^{3}}{105}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)^2*sin(x)^5,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.3685, size = 26, normalized size = 1.04 \[ -\frac{1}{7} \, \cos \left (x\right )^{7} + \frac{2}{5} \, \cos \left (x\right )^{5} - \frac{1}{3} \, \cos \left (x\right )^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^2*sin(x)^5,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.226975, size = 26, normalized size = 1.04 \[ -\frac{1}{7} \, \cos \left (x\right )^{7} + \frac{2}{5} \, \cos \left (x\right )^{5} - \frac{1}{3} \, \cos \left (x\right )^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^2*sin(x)^5,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.050655, size = 20, normalized size = 0.8 \[ - \frac{\cos ^{7}{\left (x \right )}}{7} + \frac{2 \cos ^{5}{\left (x \right )}}{5} - \frac{\cos ^{3}{\left (x \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)**2*sin(x)**5,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.205304, size = 26, normalized size = 1.04 \[ -\frac{1}{7} \, \cos \left (x\right )^{7} + \frac{2}{5} \, \cos \left (x\right )^{5} - \frac{1}{3} \, \cos \left (x\right )^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^2*sin(x)^5,x, algorithm="giac")
[Out]