3.21 \(\int \cos (3+2 x) \, dx\)

Optimal. Leaf size=10 \[ \frac{1}{2} \sin (2 x+3) \]

[Out]

Sin[3 + 2*x]/2

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Rubi [A]  time = 0.00661853, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ \frac{1}{2} \sin (2 x+3) \]

Antiderivative was successfully verified.

[In]  Int[Cos[3 + 2*x],x]

[Out]

Sin[3 + 2*x]/2

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Rubi in Sympy [A]  time = 0.515343, size = 7, normalized size = 0.7 \[ \frac{\sin{\left (2 x + 3 \right )}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(cos(3+2*x),x)

[Out]

sin(2*x + 3)/2

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Mathematica [A]  time = 0.0027125, size = 10, normalized size = 1. \[ \frac{1}{2} \sin (2 x+3) \]

Antiderivative was successfully verified.

[In]  Integrate[Cos[3 + 2*x],x]

[Out]

Sin[3 + 2*x]/2

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Maple [A]  time = 0.007, size = 9, normalized size = 0.9 \[{\frac{\sin \left ( 3+2\,x \right ) }{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(cos(3+2*x),x)

[Out]

1/2*sin(3+2*x)

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Maxima [A]  time = 1.3664, size = 11, normalized size = 1.1 \[ \frac{1}{2} \, \sin \left (2 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*sin(2*x + 3)

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Fricas [A]  time = 0.214726, size = 11, normalized size = 1.1 \[ \frac{1}{2} \, \sin \left (2 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*sin(2*x + 3)

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Sympy [A]  time = 0.122377, size = 7, normalized size = 0.7 \[ \frac{\sin{\left (2 x + 3 \right )}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(cos(3+2*x),x)

[Out]

sin(2*x + 3)/2

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GIAC/XCAS [A]  time = 0.198078, size = 11, normalized size = 1.1 \[ \frac{1}{2} \, \sin \left (2 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*sin(2*x + 3)