Optimal. Leaf size=16 \[ \frac{e^{x^2}}{2 \left (x^2+1\right )} \]
[Out]
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Rubi [A] time = 0.0823358, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{e^{x^2}}{2 \left (x^2+1\right )} \]
Antiderivative was successfully verified.
[In] Int[(E^x^2*x^3)/(1 + x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 9.8791, size = 10, normalized size = 0.62 \[ \frac{e^{x^{2}}}{2 \left (x^{2} + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(x**2)*x**3/(x**2+1)**2,x)
[Out]
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Mathematica [A] time = 0.0100631, size = 16, normalized size = 1. \[ \frac{e^{x^2}}{2 \left (x^2+1\right )} \]
Antiderivative was successfully verified.
[In] Integrate[(E^x^2*x^3)/(1 + x^2)^2,x]
[Out]
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Maple [A] time = 0.008, size = 14, normalized size = 0.9 \[{\frac{{{\rm e}^{{x}^{2}}}}{2\,{x}^{2}+2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(x^2)*x^3/(x^2+1)^2,x)
[Out]
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Maxima [A] time = 0.772056, size = 18, normalized size = 1.12 \[ \frac{e^{\left (x^{2}\right )}}{2 \,{\left (x^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*e^(x^2)/(x^2 + 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216306, size = 18, normalized size = 1.12 \[ \frac{e^{\left (x^{2}\right )}}{2 \,{\left (x^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*e^(x^2)/(x^2 + 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.07536, size = 10, normalized size = 0.62 \[ \frac{e^{x^{2}}}{2 x^{2} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(x**2)*x**3/(x**2+1)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.227179, size = 18, normalized size = 1.12 \[ \frac{e^{\left (x^{2}\right )}}{2 \,{\left (x^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*e^(x^2)/(x^2 + 1)^2,x, algorithm="giac")
[Out]