3.280 \(\int \sin (\pi x) \, dx\)

Optimal. Leaf size=9 \[ -\frac{\cos (\pi x)}{\pi } \]

[Out]

-(Cos[Pi*x]/Pi)

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Rubi [A]  time = 0.00805845, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ -\frac{\cos (\pi x)}{\pi } \]

Antiderivative was successfully verified.

[In]  Int[Sin[Pi*x],x]

[Out]

-(Cos[Pi*x]/Pi)

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Rubi in Sympy [A]  time = 0.466595, size = 7, normalized size = 0.78 \[ - \frac{\cos{\left (\pi x \right )}}{\pi } \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(sin(pi*x),x)

[Out]

-cos(pi*x)/pi

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Mathematica [A]  time = 0.00536931, size = 9, normalized size = 1. \[ -\frac{\cos (\pi x)}{\pi } \]

Antiderivative was successfully verified.

[In]  Integrate[Sin[Pi*x],x]

[Out]

-(Cos[Pi*x]/Pi)

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Maple [A]  time = 0.004, size = 10, normalized size = 1.1 \[ -{\frac{\cos \left ( \pi \,x \right ) }{\pi }} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(sin(Pi*x),x)

[Out]

-cos(Pi*x)/Pi

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Maxima [A]  time = 1.33547, size = 12, normalized size = 1.33 \[ -\frac{\cos \left (\pi x\right )}{\pi } \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sin(pi*x),x, algorithm="maxima")

[Out]

-cos(pi*x)/pi

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Fricas [A]  time = 0.211506, size = 12, normalized size = 1.33 \[ -\frac{\cos \left (\pi x\right )}{\pi } \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sin(pi*x),x, algorithm="fricas")

[Out]

-cos(pi*x)/pi

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Sympy [A]  time = 0.035801, size = 7, normalized size = 0.78 \[ - \frac{\cos{\left (\pi x \right )}}{\pi } \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sin(pi*x),x)

[Out]

-cos(pi*x)/pi

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GIAC/XCAS [A]  time = 0.216723, size = 12, normalized size = 1.33 \[ -\frac{\cos \left (\pi x\right )}{\pi } \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sin(pi*x),x, algorithm="giac")

[Out]

-cos(pi*x)/pi