Optimal. Leaf size=30 \[ \frac{x^3}{3}+\frac{x}{2}+2 \sin (x)-2 x \cos (x)-\frac{1}{2} \sin (x) \cos (x) \]
[Out]
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Rubi [A] time = 0.0527617, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 5, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.833 \[ \frac{x^3}{3}+\frac{x}{2}+2 \sin (x)-2 x \cos (x)-\frac{1}{2} \sin (x) \cos (x) \]
Antiderivative was successfully verified.
[In] Int[(x + Sin[x])^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \left (x + \sin{\left (x \right )}\right )^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x+sin(x))**2,x)
[Out]
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Mathematica [A] time = 0.0629458, size = 30, normalized size = 1. \[ \frac{1}{6} x \left (2 x^2+3\right )+2 \sin (x)-\frac{1}{4} \sin (2 x)-2 x \cos (x) \]
Antiderivative was successfully verified.
[In] Integrate[(x + Sin[x])^2,x]
[Out]
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Maple [A] time = 0.014, size = 25, normalized size = 0.8 \[{\frac{x}{2}}+{\frac{{x}^{3}}{3}}-2\,x\cos \left ( x \right ) +2\,\sin \left ( x \right ) -{\frac{\cos \left ( x \right ) \sin \left ( x \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x+sin(x))^2,x)
[Out]
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Maxima [A] time = 1.44905, size = 32, normalized size = 1.07 \[ \frac{1}{3} \, x^{3} - 2 \, x \cos \left (x\right ) + \frac{1}{2} \, x - \frac{1}{4} \, \sin \left (2 \, x\right ) + 2 \, \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + sin(x))^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220219, size = 30, normalized size = 1. \[ \frac{1}{3} \, x^{3} - 2 \, x \cos \left (x\right ) - \frac{1}{2} \,{\left (\cos \left (x\right ) - 4\right )} \sin \left (x\right ) + \frac{1}{2} \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + sin(x))^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.235873, size = 41, normalized size = 1.37 \[ \frac{x^{3}}{3} + \frac{x \sin ^{2}{\left (x \right )}}{2} + \frac{x \cos ^{2}{\left (x \right )}}{2} - 2 x \cos{\left (x \right )} - \frac{\sin{\left (x \right )} \cos{\left (x \right )}}{2} + 2 \sin{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x+sin(x))**2,x)
[Out]
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GIAC/XCAS [A] time = 0.211972, size = 32, normalized size = 1.07 \[ \frac{1}{3} \, x^{3} - 2 \, x \cos \left (x\right ) + \frac{1}{2} \, x - \frac{1}{4} \, \sin \left (2 \, x\right ) + 2 \, \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + sin(x))^2,x, algorithm="giac")
[Out]