\(\int \frac {\sin (x^5)}{x} \, dx\) [921]

Optimal result

Integrand size = 8, antiderivative size = 8 \[ \int \frac {\sin \left (x^5\right )}{x} \, dx=\frac {\text {Si}\left (x^5\right )}{5} \]

[Out]

1/5*Si(x^5)

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {3456} \[ \int \frac {\sin \left (x^5\right )}{x} \, dx=\frac {\text {Si}\left (x^5\right )}{5} \]

[In]

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

[Out]

SinIntegral[x^5]/5

Rule 3456

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

Rubi steps \begin{align*} \text {integral}& = \frac {\text {Si}\left (x^5\right )}{5} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {\sin \left (x^5\right )}{x} \, dx=\frac {\text {Si}\left (x^5\right )}{5} \]

[In]

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

[Out]

SinIntegral[x^5]/5

Maple [A] (verified)

Time = 0.29 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88

method	result	size
derivativedivides	\(\frac {\operatorname {Si}\left (x^{5}\right )}{5}\)	\(7\)
default	\(\frac {\operatorname {Si}\left (x^{5}\right )}{5}\)	\(7\)
meijerg	\(\frac {\operatorname {Si}\left (x^{5}\right )}{5}\)	\(7\)

[In]

int(sin(x^5)/x,x,method=_RETURNVERBOSE)

[Out]

1/5*Si(x^5)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int \frac {\sin \left (x^5\right )}{x} \, dx=\frac {1}{5} \, \operatorname {Si}\left (x^{5}\right ) \]

[In]

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

[Out]

1/5*sin_integral(x^5)

Sympy [A] (verification not implemented)

Time = 0.34 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.62 \[ \int \frac {\sin \left (x^5\right )}{x} \, dx=\frac {\operatorname {Si}{\left (x^{5} \right )}}{5} \]

[In]

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

[Out]

Si(x**5)/5

Maxima [C] (verification not implemented)

Result contains complex when optimal does not.

Time = 0.23 (sec) , antiderivative size = 17, normalized size of antiderivative = 2.12 \[ \int \frac {\sin \left (x^5\right )}{x} \, dx=-\frac {1}{10} i \, {\rm Ei}\left (i \, x^{5}\right ) + \frac {1}{10} i \, {\rm Ei}\left (-i \, x^{5}\right ) \]

[In]

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

[Out]

-1/10*I*Ei(I*x^5) + 1/10*I*Ei(-I*x^5)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int \frac {\sin \left (x^5\right )}{x} \, dx=\frac {1}{5} \, \operatorname {Si}\left (x^{5}\right ) \]

[In]

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

[Out]

1/5*sin_integral(x^5)

Mupad [F(-1)]

Timed out. \[ \int \frac {\sin \left (x^5\right )}{x} \, dx=\frac {\mathrm {sinint}\left (x^5\right )}{5} \]

[In]

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

[Out]

sinint(x^5)/5