3.11 \(\int \frac{\sin (y)}{y} \, dy\)

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

[Out]

SinIntegral[y]

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Rubi [A]  time = 0.018495, 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 \[ \text{Si}(y) \]

Antiderivative was successfully verified.

[In]  Int[Sin[y]/y,y]

[Out]

SinIntegral[y]

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Rubi in Sympy [A]  time = 0.697378, size = 2, normalized size = 1. \[ \operatorname{Si}{\left (y \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(sin(y)/y,y)

[Out]

Si(y)

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Mathematica [A]  time = 0.00816405, size = 2, normalized size = 1. \[ \text{Si}(y) \]

Antiderivative was successfully verified.

[In]  Integrate[Sin[y]/y,y]

[Out]

SinIntegral[y]

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Maple [A]  time = 0.001, size = 3, normalized size = 1.5 \[{\it Si} \left ( y \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(sin(y)/y,y)

[Out]

Si(y)

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Maxima [A]  time = 1.48743, size = 18, normalized size = 9. \[ -\frac{1}{2} i \,{\rm Ei}\left (i \, y\right ) + \frac{1}{2} i \,{\rm Ei}\left (-i \, y\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sin(y)/y,y, algorithm="maxima")

[Out]

-1/2*I*Ei(I*y) + 1/2*I*Ei(-I*y)

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Fricas [F]  time = 0., size = 0, normalized size = 0. \[ \operatorname{Si}\left (y\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sin(y)/y,y, algorithm="fricas")

[Out]

sin_integral(y)

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Sympy [A]  time = 0.828821, size = 2, normalized size = 1. \[ \operatorname{Si}{\left (y \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sin(y)/y,y)

[Out]

Si(y)

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GIAC/XCAS [A]  time = 0.198507, size = 3, normalized size = 1.5 \[{\rm Si}\left (y\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sin(y)/y,y, algorithm="giac")

[Out]

Si(y)