3.21 \(\int x \cos (x) \, dx\)

Optimal. Leaf size=7 \[ x \sin (x)+\cos (x) \]

[Out]

Cos[x] + x*Sin[x]

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Rubi [A]  time = 0.0135401, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ x \sin (x)+\cos (x) \]

Antiderivative was successfully verified.

[In]  Int[x*Cos[x],x]

[Out]

Cos[x] + x*Sin[x]

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Rubi in Sympy [A]  time = 0.779238, size = 7, normalized size = 1. \[ x \sin{\left (x \right )} + \cos{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x*cos(x),x)

[Out]

x*sin(x) + cos(x)

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Mathematica [A]  time = 0.00356333, size = 7, normalized size = 1. \[ x \sin (x)+\cos (x) \]

Antiderivative was successfully verified.

[In]  Integrate[x*Cos[x],x]

[Out]

Cos[x] + x*Sin[x]

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Maple [A]  time = 0., size = 8, normalized size = 1.1 \[ \cos \left ( x \right ) +x\sin \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x*cos(x),x)

[Out]

cos(x)+x*sin(x)

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Maxima [A]  time = 1.34618, size = 9, normalized size = 1.29 \[ x \sin \left (x\right ) + \cos \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x*sin(x) + cos(x)

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Fricas [A]  time = 0.228681, size = 9, normalized size = 1.29 \[ x \sin \left (x\right ) + \cos \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x*sin(x) + cos(x)

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Sympy [A]  time = 0.178842, size = 7, normalized size = 1. \[ x \sin{\left (x \right )} + \cos{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*cos(x),x)

[Out]

x*sin(x) + cos(x)

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GIAC/XCAS [A]  time = 0.198707, size = 9, normalized size = 1.29 \[ x \sin \left (x\right ) + \cos \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x*sin(x) + cos(x)