Optimal. Leaf size=33 \[ \frac{\sin ^3(x)}{9}+\frac{2 \sin (x)}{3}-\frac{2}{3} x \cos (x)-\frac{1}{3} x \sin ^2(x) \cos (x) \]
[Out]
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Rubi [A] time = 0.0338782, antiderivative size = 33, 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 \[ \frac{\sin ^3(x)}{9}+\frac{2 \sin (x)}{3}-\frac{2}{3} x \cos (x)-\frac{1}{3} x \sin ^2(x) \cos (x) \]
Antiderivative was successfully verified.
[In] Int[x*Sin[x]^3,x]
[Out]
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Rubi in Sympy [A] time = 1.36319, size = 32, normalized size = 0.97 \[ - \frac{x \sin ^{2}{\left (x \right )} \cos{\left (x \right )}}{3} - \frac{2 x \cos{\left (x \right )}}{3} + \frac{\sin ^{3}{\left (x \right )}}{9} + \frac{2 \sin{\left (x \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*sin(x)**3,x)
[Out]
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Mathematica [A] time = 0.0063939, size = 31, normalized size = 0.94 \[ \frac{3 \sin (x)}{4}-\frac{1}{36} \sin (3 x)-\frac{3}{4} x \cos (x)+\frac{1}{12} x \cos (3 x) \]
Antiderivative was successfully verified.
[In] Integrate[x*Sin[x]^3,x]
[Out]
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Maple [A] time = 0.02, size = 23, normalized size = 0.7 \[ -{\frac{x \left ( 2+ \left ( \sin \left ( x \right ) \right ) ^{2} \right ) \cos \left ( x \right ) }{3}}+{\frac{ \left ( \sin \left ( x \right ) \right ) ^{3}}{9}}+{\frac{2\,\sin \left ( x \right ) }{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*sin(x)^3,x)
[Out]
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Maxima [A] time = 1.42682, size = 31, normalized size = 0.94 \[ \frac{1}{12} \, x \cos \left (3 \, x\right ) - \frac{3}{4} \, x \cos \left (x\right ) - \frac{1}{36} \, \sin \left (3 \, x\right ) + \frac{3}{4} \, \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*sin(x)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228395, size = 31, normalized size = 0.94 \[ \frac{1}{3} \, x \cos \left (x\right )^{3} - x \cos \left (x\right ) - \frac{1}{9} \,{\left (\cos \left (x\right )^{2} - 7\right )} \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*sin(x)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.817574, size = 39, normalized size = 1.18 \[ - x \sin ^{2}{\left (x \right )} \cos{\left (x \right )} - \frac{2 x \cos ^{3}{\left (x \right )}}{3} + \frac{7 \sin ^{3}{\left (x \right )}}{9} + \frac{2 \sin{\left (x \right )} \cos ^{2}{\left (x \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*sin(x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.201063, size = 31, normalized size = 0.94 \[ \frac{1}{12} \, x \cos \left (3 \, x\right ) - \frac{3}{4} \, x \cos \left (x\right ) - \frac{1}{36} \, \sin \left (3 \, x\right ) + \frac{3}{4} \, \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*sin(x)^3,x, algorithm="giac")
[Out]