3.169 \(\int \frac{e^{1-e^{x^2} x+2 x^2} \left (x+2 x^3\right )}{\left (1-e^{x^2} x\right )^2} \, dx\)

Optimal. Leaf size=25 \[ -\frac{e^{1-e^{x^2} x}}{e^{x^2} x-1} \]

[Out]

-(E^(1 - E^x^2*x)/(-1 + E^x^2*x))

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Rubi [F]  time = 1.53434, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (\frac{e^{1-e^{x^2} x+2 x^2} \left (x+2 x^3\right )}{\left (1-e^{x^2} x\right )^2},x\right ) \]

Verification is Not applicable to the result.

[In]  Int[(E^(1 - E^x^2*x + 2*x^2)*(x + 2*x^3))/(1 - E^x^2*x)^2,x]

[Out]

Defer[Int][(E^(1 - E^x^2*x + 2*x^2)*x)/(-1 + E^x^2*x)^2, x] + 2*Defer[Int][(E^(1
- E^x^2*x + 2*x^2)*x^3)/(-1 + E^x^2*x)^2, x]

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Rubi in Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(1-exp(x**2)*x+2*x**2)*(2*x**3+x)/(1-exp(x**2)*x)**2,x)

[Out]

Timed out

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Mathematica [A]  time = 0.0405127, size = 25, normalized size = 1. \[ -\frac{e^{1-e^{x^2} x}}{e^{x^2} x-1} \]

Antiderivative was successfully verified.

[In]  Integrate[(E^(1 - E^x^2*x + 2*x^2)*(x + 2*x^3))/(1 - E^x^2*x)^2,x]

[Out]

-(E^(1 - E^x^2*x)/(-1 + E^x^2*x))

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Maple [A]  time = 0.041, size = 23, normalized size = 0.9 \[ -{\frac{{{\rm e}^{1-{{\rm e}^{{x}^{2}}}x}}}{-1+{{\rm e}^{{x}^{2}}}x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(1-exp(x^2)*x+2*x^2)*(2*x^3+x)/(1-exp(x^2)*x)^2,x)

[Out]

-exp(1-exp(x^2)*x)/(-1+exp(x^2)*x)

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Maxima [A]  time = 1.94034, size = 30, normalized size = 1.2 \[ -\frac{e^{\left (-x e^{\left (x^{2}\right )} + 1\right )}}{x e^{\left (x^{2}\right )} - 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x^3 + x)*e^(2*x^2 - x*e^(x^2) + 1)/(x*e^(x^2) - 1)^2,x, algorithm="maxima")

[Out]

-e^(-x*e^(x^2) + 1)/(x*e^(x^2) - 1)

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Fricas [A]  time = 0.226716, size = 49, normalized size = 1.96 \[ -\frac{e^{\left (2 \, x^{2} - x e^{\left (x^{2}\right )} + 1\right )}}{x e^{\left (3 \, x^{2}\right )} - e^{\left (2 \, x^{2}\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x^3 + x)*e^(2*x^2 - x*e^(x^2) + 1)/(x*e^(x^2) - 1)^2,x, algorithm="fricas")

[Out]

-e^(2*x^2 - x*e^(x^2) + 1)/(x*e^(3*x^2) - e^(2*x^2))

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Sympy [A]  time = 0.640331, size = 31, normalized size = 1.24 \[ - \frac{e^{2 x^{2} - x e^{x^{2}} + 1}}{x e^{3 x^{2}} - e^{2 x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(1-exp(x**2)*x+2*x**2)*(2*x**3+x)/(1-exp(x**2)*x)**2,x)

[Out]

-exp(2*x**2 - x*exp(x**2) + 1)/(x*exp(3*x**2) - exp(2*x**2))

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (2 \, x^{3} + x\right )} e^{\left (2 \, x^{2} - x e^{\left (x^{2}\right )} + 1\right )}}{{\left (x e^{\left (x^{2}\right )} - 1\right )}^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x^3 + x)*e^(2*x^2 - x*e^(x^2) + 1)/(x*e^(x^2) - 1)^2,x, algorithm="giac")

[Out]

integrate((2*x^3 + x)*e^(2*x^2 - x*e^(x^2) + 1)/(x*e^(x^2) - 1)^2, x)