Optimal. Leaf size=50 \[ \frac{1}{2} e^x x^2 \sin (x)-\frac{1}{2} e^x x^2 \cos (x)-\frac{1}{2} e^x \sin (x)+e^x x \cos (x)-\frac{1}{2} e^x \cos (x) \]
[Out]
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Rubi [A] time = 0.167055, antiderivative size = 50, normalized size of antiderivative = 1., number of steps used = 11, number of rules used = 5, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.556 \[ \frac{1}{2} e^x x^2 \sin (x)-\frac{1}{2} e^x x^2 \cos (x)-\frac{1}{2} e^x \sin (x)+e^x x \cos (x)-\frac{1}{2} e^x \cos (x) \]
Antiderivative was successfully verified.
[In] Int[E^x*x^2*Sin[x],x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x^{2} e^{x} \sin{\left (x \right )}}{2} - \frac{x^{2} e^{x} \cos{\left (x \right )}}{2} - 2 \int x \left (\frac{e^{x} \sin{\left (x \right )}}{2} - \frac{e^{x} \cos{\left (x \right )}}{2}\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(x)*x**2*sin(x),x)
[Out]
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Mathematica [A] time = 0.0431513, size = 25, normalized size = 0.5 \[ \frac{1}{2} e^x \left (\left (x^2-1\right ) \sin (x)-(x-1)^2 \cos (x)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[E^x*x^2*Sin[x],x]
[Out]
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Maple [A] time = 0.008, size = 27, normalized size = 0.5 \[ \left ( -{\frac{{x}^{2}}{2}}+x-{\frac{1}{2}} \right ){{\rm e}^{x}}\cos \left ( x \right ) + \left ({\frac{{x}^{2}}{2}}-{\frac{1}{2}} \right ){{\rm e}^{x}}\sin \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(x)*x^2*sin(x),x)
[Out]
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Maxima [A] time = 1.3933, size = 35, normalized size = 0.7 \[ -\frac{1}{2} \,{\left (x^{2} - 2 \, x + 1\right )} \cos \left (x\right ) e^{x} + \frac{1}{2} \,{\left (x^{2} - 1\right )} e^{x} \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^x*sin(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 6.30064, size = 35, normalized size = 0.7 \[ -\frac{1}{2} \,{\left (x^{2} - 2 \, x + 1\right )} \cos \left (x\right ) e^{x} + \frac{1}{2} \,{\left (x^{2} - 1\right )} e^{x} \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^x*sin(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.21248, size = 48, normalized size = 0.96 \[ \frac{x^{2} e^{x} \sin{\left (x \right )}}{2} - \frac{x^{2} e^{x} \cos{\left (x \right )}}{2} + x e^{x} \cos{\left (x \right )} - \frac{e^{x} \sin{\left (x \right )}}{2} - \frac{e^{x} \cos{\left (x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(x)*x**2*sin(x),x)
[Out]
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GIAC/XCAS [A] time = 0.198486, size = 34, normalized size = 0.68 \[ -\frac{1}{2} \,{\left ({\left (x^{2} - 2 \, x + 1\right )} \cos \left (x\right ) -{\left (x^{2} - 1\right )} \sin \left (x\right )\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^x*sin(x),x, algorithm="giac")
[Out]