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

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

[Out]

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

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, 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*}

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Mathematica [A]  time = 0.01, size = 10, normalized size = 1.00 \[ \frac {1}{2} \sin (2 x+3) \]

Antiderivative was successfully verified.

[In]

Integrate[Cos[3 + 2*x],x]

[Out]

Sin[3 + 2*x]/2

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fricas [A]  time = 0.43, size = 8, normalized size = 0.80 \[ \frac {1}{2} \, \sin \left (2 \, x + 3\right ) \]

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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giac [A]  time = 1.04, size = 8, normalized size = 0.80 \[ \frac {1}{2} \, \sin \left (2 \, x + 3\right ) \]

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)

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maple [A]  time = 0.02, size = 9, normalized size = 0.90 \[ \frac {\sin \left (2 x +3\right )}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cos(2*x+3),x)

[Out]

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

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maxima [A]  time = 0.52, size = 8, normalized size = 0.80 \[ \frac {1}{2} \, \sin \left (2 \, x + 3\right ) \]

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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mupad [B]  time = 0.07, size = 8, normalized size = 0.80 \[ \frac {\sin \left (2\,x+3\right )}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cos(2*x + 3),x)

[Out]

sin(2*x + 3)/2

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sympy [A]  time = 0.12, size = 7, normalized size = 0.70 \[ \frac {\sin {\left (2 x + 3 \right )}}{2} \]

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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