\(\int \frac {\sin (x)}{x} \, dx\) [9]

Optimal result

Integrand size = 6, antiderivative size = 2 \[ \int \frac {\sin (x)}{x} \, dx=\text {Si}(x) \]

[Out]

Si(x)

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {3380} \[ \int \frac {\sin (x)}{x} \, dx=\text {Si}(x) \]

[In]

Int[Sin[x]/x,x]

[Out]

SinIntegral[x]

Rule 3380

Int[sin[(e_.) + (f_.)*(x_)]/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[SinIntegral[e + f*x]/d, x] /; FreeQ[{c, d,
e, f}, x] && EqQ[d*e - c*f, 0]

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

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {\sin (x)}{x} \, dx=\text {Si}(x) \]

[In]

Integrate[Sin[x]/x,x]

[Out]

SinIntegral[x]

Maple [A] (verified)

Time = 0.08 (sec) , antiderivative size = 3, normalized size of antiderivative = 1.50

method	result	size
default	\(\operatorname {Si}\left (x \right )\)	\(3\)
meijerg	\(\operatorname {Si}\left (x \right )\)	\(3\)
risch	\(-\frac {\pi \,\operatorname {csgn}\left (x \right )}{2}+\operatorname {Si}\left (x \right )\)	\(9\)

[In]

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

[Out]

Si(x)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {\sin (x)}{x} \, dx=\operatorname {Si}\left (x\right ) \]

[In]

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

[Out]

sin_integral(x)

Sympy [A] (verification not implemented)

Time = 0.46 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {\sin (x)}{x} \, dx=\operatorname {Si}{\left (x \right )} \]

[In]

integrate(sin(x)/x,x)

[Out]

Si(x)

Maxima [C] (verification not implemented)

Result contains complex when optimal does not.

Time = 0.24 (sec) , antiderivative size = 13, normalized size of antiderivative = 6.50 \[ \int \frac {\sin (x)}{x} \, dx=-\frac {1}{2} i \, {\rm Ei}\left (i \, x\right ) + \frac {1}{2} i \, {\rm Ei}\left (-i \, x\right ) \]

[In]

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

[Out]

-1/2*I*Ei(I*x) + 1/2*I*Ei(-I*x)

Giac [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {\sin (x)}{x} \, dx=\operatorname {Si}\left (x\right ) \]

[In]

integrate(sin(x)/x,x, algorithm="giac")

[Out]

sin_integral(x)

Mupad [F(-1)]

Timed out. \[ \int \frac {\sin (x)}{x} \, dx=\mathrm {sinint}\left (x\right ) \]

[In]

int(sin(x)/x,x)

[Out]

sinint(x)