3.921 \(\int \frac{\sin (x^5)}{x} \, dx\)

Optimal. Leaf size=8 \[ \frac{\text{Si}\left (x^5\right )}{5} \]

[Out]

SinIntegral[x^5]/5

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Rubi [A]  time = 0.0065648, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125, Rules used = {3375} \[ \frac{\text{Si}\left (x^5\right )}{5} \]

Antiderivative was successfully verified.

[In]

Int[Sin[x^5]/x,x]

[Out]

SinIntegral[x^5]/5

Rule 3375

Int[Sin[(d_.)*(x_)^(n_)]/(x_), x_Symbol] :> Simp[SinIntegral[d*x^n]/n, x] /; FreeQ[{d, n}, x]

Rubi steps

\begin{align*} \int \frac{\sin \left (x^5\right )}{x} \, dx &=\frac{\text{Si}\left (x^5\right )}{5}\\ \end{align*}

Mathematica [A]  time = 0.0019638, size = 8, normalized size = 1. \[ \frac{\text{Si}\left (x^5\right )}{5} \]

Antiderivative was successfully verified.

[In]

Integrate[Sin[x^5]/x,x]

[Out]

SinIntegral[x^5]/5

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Maple [A]  time = 0.005, size = 7, normalized size = 0.9 \begin{align*}{\frac{{\it Si} \left ({x}^{5} \right ) }{5}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sin(x^5)/x,x)

[Out]

1/5*Si(x^5)

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Maxima [C]  time = 1.08548, size = 23, normalized size = 2.88 \begin{align*} -\frac{1}{10} i \,{\rm Ei}\left (i \, x^{5}\right ) + \frac{1}{10} i \,{\rm Ei}\left (-i \, x^{5}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sin(x^5)/x,x, algorithm="maxima")

[Out]

-1/10*I*Ei(I*x^5) + 1/10*I*Ei(-I*x^5)

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Fricas [A]  time = 1.98848, size = 31, normalized size = 3.88 \begin{align*} \frac{1}{5} \, \operatorname{Si}\left (x^{5}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sin(x^5)/x,x, algorithm="fricas")

[Out]

1/5*sin_integral(x^5)

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Sympy [A]  time = 0.571996, size = 5, normalized size = 0.62 \begin{align*} \frac{\operatorname{Si}{\left (x^{5} \right )}}{5} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sin(x**5)/x,x)

[Out]

Si(x**5)/5

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Giac [A]  time = 1.10321, size = 8, normalized size = 1. \begin{align*} \frac{1}{5} \, \operatorname{Si}\left (x^{5}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sin(x^5)/x,x, algorithm="giac")

[Out]

1/5*sin_integral(x^5)