3.76 \(\int \sin (x) \, dx\)

Optimal. Leaf size=4 \[ -\cos (x) \]

[Out]

-Cos[x]

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Rubi [A]  time = 0.0049239, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 2, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ -\cos (x) \]

Antiderivative was successfully verified.

[In]  Int[Sin[x],x]

[Out]

-Cos[x]

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Rubi in Sympy [A]  time = 0.027205, size = 3, normalized size = 0.75 \[ - \cos{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(sin(x),x)

[Out]

-cos(x)

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Mathematica [A]  time = 0.00416458, size = 4, normalized size = 1. \[ -\cos (x) \]

Antiderivative was successfully verified.

[In]  Integrate[Sin[x],x]

[Out]

-Cos[x]

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Maple [A]  time = 0.001, size = 5, normalized size = 1.3 \[ -\cos \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(sin(x),x)

[Out]

-cos(x)

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Maxima [A]  time = 1.40122, size = 5, normalized size = 1.25 \[ -\cos \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-cos(x)

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Fricas [A]  time = 0.227302, size = 5, normalized size = 1.25 \[ -\cos \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-cos(x)

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Sympy [A]  time = 0.03024, size = 3, normalized size = 0.75 \[ - \cos{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sin(x),x)

[Out]

-cos(x)

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GIAC/XCAS [A]  time = 0.198074, size = 5, normalized size = 1.25 \[ -\cos \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-cos(x)