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

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

[Out]

1/5*Si(x^5)

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Rubi [A]  time = 0.01, antiderivative size = 8, normalized size of antiderivative = 1.00, 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*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 1.00 \[ \frac {\text {Si}\left (x^5\right )}{5} \]

Antiderivative was successfully verified.

[In]

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

[Out]

SinIntegral[x^5]/5

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fricas [A]  time = 0.73, size = 6, normalized size = 0.75 \[ \frac {1}{5} \, \operatorname {Si}\left (x^{5}\right ) \]

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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giac [A]  time = 0.13, size = 6, normalized size = 0.75 \[ \frac {1}{5} \, \operatorname {Si}\left (x^{5}\right ) \]

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)

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maple [A]  time = 0.03, size = 7, normalized size = 0.88 \[ \frac {\Si \left (x^{5}\right )}{5} \]

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 = 0.36, size = 17, normalized size = 2.12 \[ -\frac {1}{10} i \, {\rm Ei}\left (i \, x^{5}\right ) + \frac {1}{10} i \, {\rm Ei}\left (-i \, x^{5}\right ) \]

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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mupad [F]  time = 0.00, size = -1, normalized size = -0.12 \[ \frac {\mathrm {sinint}\left (x^5\right )}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

sinint(x^5)/5

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sympy [A]  time = 0.64, size = 5, normalized size = 0.62 \[ \frac {\operatorname {Si}{\left (x^{5} \right )}}{5} \]

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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