Optimal. Leaf size=28 \[ \frac{1}{4} x \sin (3)-\frac{1}{4} \cos (2 x+3)-\frac{1}{16} \cos (4 x+3) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0381084, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{1}{4} x \sin (3)-\frac{1}{4} \cos (2 x+3)-\frac{1}{16} \cos (4 x+3) \]
Antiderivative was successfully verified.
[In] Int[Cos[x]^2*Sin[3 + 2*x],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{\cos{\left (2 x + 3 \right )}}{4} - \frac{\cos{\left (4 x + 3 \right )}}{16} + \sin{\left (3 \right )} \int \frac{1}{4}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)**2*sin(3+2*x),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0142453, size = 28, normalized size = 1. \[ \frac{1}{4} x \sin (3)-\frac{1}{4} \cos (2 x+3)-\frac{1}{16} \cos (4 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]^2*Sin[3 + 2*x],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 23, normalized size = 0.8 \[ -{\frac{\cos \left ( 3+2\,x \right ) }{4}}-{\frac{\cos \left ( 3+4\,x \right ) }{16}}+{\frac{x\sin \left ( 3 \right ) }{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)^2*sin(3+2*x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33387, size = 30, normalized size = 1.07 \[ \frac{1}{4} \, x \sin \left (3\right ) - \frac{1}{16} \, \cos \left (4 \, x + 3\right ) - \frac{1}{4} \, \cos \left (2 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^2*sin(2*x + 3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.227144, size = 43, normalized size = 1.54 \[ -\frac{1}{2} \, \cos \left (3\right ) \cos \left (x\right )^{4} + \frac{1}{4} \, x \sin \left (3\right ) + \frac{1}{4} \,{\left (2 \, \cos \left (x\right )^{3} \sin \left (3\right ) + \cos \left (x\right ) \sin \left (3\right )\right )} \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^2*sin(2*x + 3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 3.05223, size = 76, normalized size = 2.71 \[ - \frac{x \sin ^{2}{\left (x \right )} \sin{\left (2 x + 3 \right )}}{4} - \frac{x \sin{\left (x \right )} \cos{\left (x \right )} \cos{\left (2 x + 3 \right )}}{2} + \frac{x \sin{\left (2 x + 3 \right )} \cos ^{2}{\left (x \right )}}{4} - \frac{\sin ^{2}{\left (x \right )} \cos{\left (2 x + 3 \right )}}{2} + \frac{3 \sin{\left (x \right )} \sin{\left (2 x + 3 \right )} \cos{\left (x \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)**2*sin(3+2*x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.211553, size = 30, normalized size = 1.07 \[ \frac{1}{4} \, x \sin \left (3\right ) - \frac{1}{16} \, \cos \left (4 \, x + 3\right ) - \frac{1}{4} \, \cos \left (2 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^2*sin(2*x + 3),x, algorithm="giac")
[Out]