3.77 \(\int \cos (x) \, dx\)

Optimal. Leaf size=2 \[ \sin (x) \]

[Out]

sin(x)

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Rubi [A]  time = 0.00, antiderivative size = 2, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {2637} \[ \sin (x) \]

Antiderivative was successfully verified.

[In]

Int[Cos[x],x]

[Out]

Sin[x]

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 (x) \, dx &=\sin (x)\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 2, normalized size = 1.00 \[ \sin (x) \]

Antiderivative was successfully verified.

[In]

Integrate[Cos[x],x]

[Out]

Sin[x]

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fricas [A]  time = 0.42, size = 2, normalized size = 1.00 \[ \sin \relax (x) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(x),x, algorithm="fricas")

[Out]

sin(x)

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giac [A]  time = 0.96, size = 2, normalized size = 1.00 \[ \sin \relax (x) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(x),x, algorithm="giac")

[Out]

sin(x)

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maple [A]  time = 0.00, size = 3, normalized size = 1.50 \[ \sin \relax (x ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cos(x),x)

[Out]

sin(x)

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maxima [A]  time = 0.41, size = 2, normalized size = 1.00 \[ \sin \relax (x) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(x),x, algorithm="maxima")

[Out]

sin(x)

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mupad [B]  time = 0.03, size = 2, normalized size = 1.00 \[ \sin \relax (x) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cos(x),x)

[Out]

sin(x)

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sympy [A]  time = 0.06, size = 2, normalized size = 1.00 \[ \sin {\relax (x )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(x),x)

[Out]

sin(x)

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