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 = 0.0030981, 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, Rules used = {2637} \[ \frac{1}{2} \sin (2 x+3) \]

Antiderivative was successfully verified.

[In]

Int[Cos[3 + 2*x],x]

[Out]

Sin[3 + 2*x]/2

Rule 2637

Int[sin[Pi/2 + (c_.) + (d_.)*(x_)], x_Symbol] :> Simp[Sin[c + d*x]/d, x] /; FreeQ[{c, d}, x]

Rubi steps

\begin{align*} \int \cos (3+2 x) \, dx &=\frac{1}{2} \sin (3+2 x)\\ \end{align*}

Mathematica [A]  time = 0.0042777, 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 = 0.005, size = 9, normalized size = 0.9 \begin{align*}{\frac{\sin \left ( 3+2\,x \right ) }{2}} \end{align*}

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 = 0.925298, size = 11, normalized size = 1.1 \begin{align*} \frac{1}{2} \, \sin \left (2 \, x + 3\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*sin(2*x + 3)

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Fricas [A]  time = 1.87985, size = 24, normalized size = 2.4 \begin{align*} \frac{1}{2} \, \sin \left (2 \, x + 3\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*sin(2*x + 3)

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Sympy [A]  time = 0.111567, size = 7, normalized size = 0.7 \begin{align*} \frac{\sin{\left (2 x + 3 \right )}}{2} \end{align*}

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 [A]  time = 1.101, size = 11, normalized size = 1.1 \begin{align*} \frac{1}{2} \, \sin \left (2 \, x + 3\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*sin(2*x + 3)