Optimal. Leaf size=18 \[ \frac{1}{2} x \sin (2 x)+\frac{1}{4} \cos (2 x) \]
[Out]
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Rubi [A] time = 0.0191007, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ \frac{1}{2} x \sin (2 x)+\frac{1}{4} \cos (2 x) \]
Antiderivative was successfully verified.
[In] Int[x*Cos[2*x],x]
[Out]
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Rubi in Sympy [A] time = 0.850406, size = 14, normalized size = 0.78 \[ \frac{x \sin{\left (2 x \right )}}{2} + \frac{\cos{\left (2 x \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*cos(2*x),x)
[Out]
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Mathematica [A] time = 0.00491014, size = 18, normalized size = 1. \[ \frac{1}{2} x \sin (2 x)+\frac{1}{4} \cos (2 x) \]
Antiderivative was successfully verified.
[In] Integrate[x*Cos[2*x],x]
[Out]
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Maple [A] time = 0.007, size = 15, normalized size = 0.8 \[{\frac{\cos \left ( 2\,x \right ) }{4}}+{\frac{x\sin \left ( 2\,x \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*cos(2*x),x)
[Out]
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Maxima [A] time = 1.34922, size = 19, normalized size = 1.06 \[ \frac{1}{2} \, x \sin \left (2 \, x\right ) + \frac{1}{4} \, \cos \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*cos(2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22197, size = 19, normalized size = 1.06 \[ \frac{1}{2} \, x \sin \left (2 \, x\right ) + \frac{1}{4} \, \cos \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*cos(2*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.188105, size = 14, normalized size = 0.78 \[ \frac{x \sin{\left (2 x \right )}}{2} + \frac{\cos{\left (2 x \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*cos(2*x),x)
[Out]
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GIAC/XCAS [A] time = 0.232345, size = 19, normalized size = 1.06 \[ \frac{1}{2} \, x \sin \left (2 \, x\right ) + \frac{1}{4} \, \cos \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*cos(2*x),x, algorithm="giac")
[Out]