3.131 \(\int \cos (3 x) \sin (2 x) \, dx\)

Optimal. Leaf size=15 \[ \frac{\cos (x)}{2}-\frac{1}{10} \cos (5 x) \]

[Out]

Cos[x]/2 - Cos[5*x]/10

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Rubi [A]  time = 0.0139151, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{\cos (x)}{2}-\frac{1}{10} \cos (5 x) \]

Antiderivative was successfully verified.

[In]  Int[Cos[3*x]*Sin[2*x],x]

[Out]

Cos[x]/2 - Cos[5*x]/10

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Rubi in Sympy [A]  time = 1.05248, size = 10, normalized size = 0.67 \[ \frac{\cos{\left (x \right )}}{2} - \frac{\cos{\left (5 x \right )}}{10} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(cos(3*x)*sin(2*x),x)

[Out]

cos(x)/2 - cos(5*x)/10

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Mathematica [A]  time = 0.00869426, size = 15, normalized size = 1. \[ \frac{\cos (x)}{2}-\frac{1}{10} \cos (5 x) \]

Antiderivative was successfully verified.

[In]  Integrate[Cos[3*x]*Sin[2*x],x]

[Out]

Cos[x]/2 - Cos[5*x]/10

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Maple [A]  time = 0.025, size = 12, normalized size = 0.8 \[{\frac{\cos \left ( x \right ) }{2}}-{\frac{\cos \left ( 5\,x \right ) }{10}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(cos(3*x)*sin(2*x),x)

[Out]

1/2*cos(x)-1/10*cos(5*x)

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Maxima [A]  time = 1.37778, size = 15, normalized size = 1. \[ -\frac{1}{10} \, \cos \left (5 \, x\right ) + \frac{1}{2} \, \cos \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(cos(3*x)*sin(2*x),x, algorithm="maxima")

[Out]

-1/10*cos(5*x) + 1/2*cos(x)

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Fricas [A]  time = 0.224957, size = 18, normalized size = 1.2 \[ -\frac{8}{5} \, \cos \left (x\right )^{5} + 2 \, \cos \left (x\right )^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(cos(3*x)*sin(2*x),x, algorithm="fricas")

[Out]

-8/5*cos(x)^5 + 2*cos(x)^3

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Sympy [A]  time = 0.69644, size = 26, normalized size = 1.73 \[ \frac{3 \sin{\left (2 x \right )} \sin{\left (3 x \right )}}{5} + \frac{2 \cos{\left (2 x \right )} \cos{\left (3 x \right )}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(cos(3*x)*sin(2*x),x)

[Out]

3*sin(2*x)*sin(3*x)/5 + 2*cos(2*x)*cos(3*x)/5

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GIAC/XCAS [A]  time = 0.200464, size = 15, normalized size = 1. \[ -\frac{1}{10} \, \cos \left (5 \, x\right ) + \frac{1}{2} \, \cos \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(cos(3*x)*sin(2*x),x, algorithm="giac")

[Out]

-1/10*cos(5*x) + 1/2*cos(x)