Optimal. Leaf size=23 \[ -\frac{x}{4}+\frac{1}{2} x \sin ^2(x)+\frac{1}{4} \sin (x) \cos (x) \]
[Out]
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Rubi [A] time = 0.0204367, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ -\frac{x}{4}+\frac{1}{2} x \sin ^2(x)+\frac{1}{4} \sin (x) \cos (x) \]
Antiderivative was successfully verified.
[In] Int[x*Cos[x]*Sin[x],x]
[Out]
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Rubi in Sympy [A] time = 1.03985, size = 19, normalized size = 0.83 \[ \frac{x \sin ^{2}{\left (x \right )}}{2} - \frac{x}{4} + \frac{\sin{\left (x \right )} \cos{\left (x \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*cos(x)*sin(x),x)
[Out]
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Mathematica [A] time = 0.00437193, size = 18, normalized size = 0.78 \[ \frac{1}{8} \sin (2 x)-\frac{1}{4} x \cos (2 x) \]
Antiderivative was successfully verified.
[In] Integrate[x*Cos[x]*Sin[x],x]
[Out]
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Maple [A] time = 0.004, size = 18, normalized size = 0.8 \[ -{\frac{x \left ( \cos \left ( x \right ) \right ) ^{2}}{2}}+{\frac{\cos \left ( x \right ) \sin \left ( x \right ) }{4}}+{\frac{x}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*cos(x)*sin(x),x)
[Out]
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Maxima [A] time = 1.39561, size = 19, normalized size = 0.83 \[ -\frac{1}{4} \, x \cos \left (2 \, x\right ) + \frac{1}{8} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*cos(x)*sin(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225672, size = 23, normalized size = 1. \[ -\frac{1}{2} \, x \cos \left (x\right )^{2} + \frac{1}{4} \, \cos \left (x\right ) \sin \left (x\right ) + \frac{1}{4} \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*cos(x)*sin(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.412793, size = 24, normalized size = 1.04 \[ \frac{x \sin ^{2}{\left (x \right )}}{4} - \frac{x \cos ^{2}{\left (x \right )}}{4} + \frac{\sin{\left (x \right )} \cos{\left (x \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*cos(x)*sin(x),x)
[Out]
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GIAC/XCAS [A] time = 0.213684, size = 19, normalized size = 0.83 \[ -\frac{1}{4} \, x \cos \left (2 \, x\right ) + \frac{1}{8} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*cos(x)*sin(x),x, algorithm="giac")
[Out]