Optimal. Leaf size=17 \[ -\frac{1}{4} \cos (2 x)-\frac{1}{8} \cos (4 x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0153035, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ -\frac{1}{4} \cos (2 x)-\frac{1}{8} \cos (4 x) \]
Antiderivative was successfully verified.
[In] Int[Cos[x]*Sin[3*x],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 0.996206, size = 14, normalized size = 0.82 \[ - \frac{\cos{\left (2 x \right )}}{4} - \frac{\cos{\left (4 x \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)*sin(3*x),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00944942, size = 17, normalized size = 1. \[ -\frac{1}{2} \cos ^2(x)-\frac{1}{8} \cos (4 x) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]*Sin[3*x],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.046, size = 14, normalized size = 0.8 \[ - \left ( \cos \left ( x \right ) \right ) ^{4}+{\frac{ \left ( \cos \left ( x \right ) \right ) ^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)*sin(3*x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.36308, size = 18, normalized size = 1.06 \[ -\frac{1}{8} \, \cos \left (4 \, x\right ) - \frac{1}{4} \, \cos \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)*sin(3*x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.228532, size = 18, normalized size = 1.06 \[ -\cos \left (x\right )^{4} + \frac{1}{2} \, \cos \left (x\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)*sin(3*x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.727638, size = 22, normalized size = 1.29 \[ - \frac{\sin{\left (x \right )} \sin{\left (3 x \right )}}{8} - \frac{3 \cos{\left (x \right )} \cos{\left (3 x \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)*sin(3*x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.199836, size = 18, normalized size = 1.06 \[ -\frac{1}{8} \, \cos \left (4 \, x\right ) - \frac{1}{4} \, \cos \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)*sin(3*x),x, algorithm="giac")
[Out]