3.76 \(\int \sin (x) \, dx\)

Optimal. Leaf size=4 \[ -\cos (x) \]

[Out]

-cos(x)

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Rubi [A]  time = 0.00, antiderivative size = 4, 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 = {2638} \[ -\cos (x) \]

Antiderivative was successfully verified.

[In]

Int[Sin[x],x]

[Out]

-Cos[x]

Rule 2638

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

Rubi steps

\begin {align*} \int \sin (x) \, dx &=-\cos (x)\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 4, normalized size = 1.00 \[ -\cos (x) \]

Antiderivative was successfully verified.

[In]

Integrate[Sin[x],x]

[Out]

-Cos[x]

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fricas [A]  time = 0.42, size = 4, normalized size = 1.00 \[ -\cos \relax (x) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-cos(x)

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giac [A]  time = 1.03, size = 4, normalized size = 1.00 \[ -\cos \relax (x) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sin(x),x, algorithm="giac")

[Out]

-cos(x)

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maple [A]  time = 0.00, size = 5, normalized size = 1.25 \[ -\cos \relax (x ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sin(x),x)

[Out]

-cos(x)

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maxima [A]  time = 0.42, size = 4, normalized size = 1.00 \[ -\cos \relax (x) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-cos(x)

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mupad [B]  time = 0.02, size = 4, normalized size = 1.00 \[ -\cos \relax (x) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sin(x),x)

[Out]

-cos(x)

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sympy [A]  time = 0.06, size = 3, normalized size = 0.75 \[ - \cos {\relax (x )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sin(x),x)

[Out]

-cos(x)

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