Optimal. Leaf size=24 \[ x^3 (-\cos (x))+3 x^2 \sin (x)-6 \sin (x)+6 x \cos (x) \]
[Out]
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Rubi [A] time = 0.0522071, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ x^3 (-\cos (x))+3 x^2 \sin (x)-6 \sin (x)+6 x \cos (x) \]
Antiderivative was successfully verified.
[In] Int[x^3*Sin[x],x]
[Out]
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Rubi in Sympy [A] time = 1.92561, size = 26, normalized size = 1.08 \[ - x^{3} \cos{\left (x \right )} + 3 x^{2} \sin{\left (x \right )} + 6 x \cos{\left (x \right )} - 6 \sin{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*sin(x),x)
[Out]
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Mathematica [A] time = 0.012055, size = 20, normalized size = 0.83 \[ 3 \left (x^2-2\right ) \sin (x)-x \left (x^2-6\right ) \cos (x) \]
Antiderivative was successfully verified.
[In] Integrate[x^3*Sin[x],x]
[Out]
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Maple [A] time = 0.007, size = 25, normalized size = 1. \[ 6\,x\cos \left ( x \right ) -{x}^{3}\cos \left ( x \right ) -6\,\sin \left ( x \right ) +3\,{x}^{2}\sin \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*sin(x),x)
[Out]
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Maxima [A] time = 1.35021, size = 28, normalized size = 1.17 \[ -{\left (x^{3} - 6 \, x\right )} \cos \left (x\right ) + 3 \,{\left (x^{2} - 2\right )} \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*sin(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.242894, size = 28, normalized size = 1.17 \[ -{\left (x^{3} - 6 \, x\right )} \cos \left (x\right ) + 3 \,{\left (x^{2} - 2\right )} \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*sin(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.924283, size = 26, normalized size = 1.08 \[ - x^{3} \cos{\left (x \right )} + 3 x^{2} \sin{\left (x \right )} + 6 x \cos{\left (x \right )} - 6 \sin{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*sin(x),x)
[Out]
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GIAC/XCAS [A] time = 0.221625, size = 28, normalized size = 1.17 \[ -{\left (x^{3} - 6 \, x\right )} \cos \left (x\right ) + 3 \,{\left (x^{2} - 2\right )} \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*sin(x),x, algorithm="giac")
[Out]