\(\int \sin (x) \, dx\) [76]

Optimal result

Integrand size = 2, antiderivative size = 4 \[ \int \sin (x) \, dx=-\cos (x) \]

[Out]

-cos(x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {2718} \[ \int \sin (x) \, dx=-\cos (x) \]

[In]

Int[Sin[x],x]

[Out]

-Cos[x]

Rule 2718

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

Rubi steps \begin{align*} \text {integral}& = -\cos (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int \sin (x) \, dx=-\cos (x) \]

[In]

Integrate[Sin[x],x]

[Out]

-Cos[x]

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.25

method	result	size
lookup	\(-\cos \left (x \right )\)	\(5\)
default	\(-\cos \left (x \right )\)	\(5\)
risch	\(-\cos \left (x \right )\)	\(5\)
parallelrisch	\(-\cos \left (x \right )-1\)	\(7\)
norman	\(-\frac {2}{1+\tan ^{2}\left (\frac {x}{2}\right )}\)	\(13\)
meijerg	\(\sqrt {\pi }\, \left (\frac {1}{\sqrt {\pi }}-\frac {\cos \left (x \right )}{\sqrt {\pi }}\right )\)	\(16\)

[In]

int(sin(x),x,method=_RETURNVERBOSE)

[Out]

-cos(x)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int \sin (x) \, dx=-\cos \left (x\right ) \]

[In]

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

[Out]

-cos(x)

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.75 \[ \int \sin (x) \, dx=- \cos {\left (x \right )} \]

[In]

integrate(sin(x),x)

[Out]

-cos(x)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int \sin (x) \, dx=-\cos \left (x\right ) \]

[In]

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

[Out]

-cos(x)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int \sin (x) \, dx=-\cos \left (x\right ) \]

[In]

integrate(sin(x),x, algorithm="giac")

[Out]

-cos(x)

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int \sin (x) \, dx=-\cos \left (x\right ) \]

[In]

int(sin(x),x)

[Out]

-cos(x)