3.9 \(\int \frac{\sin (x)}{x} \, dx\)

Optimal. Leaf size=2 \[ \text{Si}(x) \]

[Out]

SinIntegral[x]

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Rubi [A]  time = 0.0114418, antiderivative size = 2, normalized size of antiderivative = 1., 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 = {3299} \[ \text{Si}(x) \]

Antiderivative was successfully verified.

[In]

Int[Sin[x]/x,x]

[Out]

SinIntegral[x]

Rule 3299

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*} \int \frac{\sin (x)}{x} \, dx &=\text{Si}(x)\\ \end{align*}

Mathematica [A]  time = 0.0107058, size = 2, normalized size = 1. \[ \text{Si}(x) \]

Antiderivative was successfully verified.

[In]

Integrate[Sin[x]/x,x]

[Out]

SinIntegral[x]

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Maple [A]  time = 0.004, size = 3, normalized size = 1.5 \begin{align*}{\it Si} \left ( x \right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sin(x)/x,x)

[Out]

Si(x)

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Maxima [C]  time = 1.09359, size = 18, normalized size = 9. \begin{align*} -\frac{1}{2} i \,{\rm Ei}\left (i \, x\right ) + \frac{1}{2} i \,{\rm Ei}\left (-i \, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/2*I*Ei(I*x) + 1/2*I*Ei(-I*x)

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Fricas [A]  time = 2.33787, size = 23, normalized size = 11.5 \begin{align*} \operatorname{Si}\left (x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

sin_integral(x)

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Sympy [A]  time = 0.563997, size = 2, normalized size = 1. \begin{align*} \operatorname{Si}{\left (x \right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sin(x)/x,x)

[Out]

Si(x)

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Giac [A]  time = 1.08616, size = 3, normalized size = 1.5 \begin{align*} \operatorname{Si}\left (x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

sin_integral(x)