3.31.14 \(\int \frac {e^{5-e^{\frac {1}{x}}+x-x^2} (e^{\frac {1}{x}}+x^2-2 x^3)}{x^2} \, dx\)

Optimal. Leaf size=17 \[ e^{5-e^{\frac {1}{x}}+x-x^2} \]

________________________________________________________________________________________

Rubi [A]  time = 0.33, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {6706} \begin {gather*} e^{-x^2+x-e^{\frac {1}{x}}+5} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^(5 - E^x^(-1) + x - x^2)*(E^x^(-1) + x^2 - 2*x^3))/x^2,x]

[Out]

E^(5 - E^x^(-1) + x - x^2)

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=e^{5-e^{\frac {1}{x}}+x-x^2}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.16, size = 17, normalized size = 1.00 \begin {gather*} e^{5-e^{\frac {1}{x}}+x-x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(5 - E^x^(-1) + x - x^2)*(E^x^(-1) + x^2 - 2*x^3))/x^2,x]

[Out]

E^(5 - E^x^(-1) + x - x^2)

________________________________________________________________________________________

fricas [A]  time = 3.00, size = 15, normalized size = 0.88 \begin {gather*} e^{\left (-x^{2} + x - e^{\frac {1}{x}} + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(1/x)-2*x^3+x^2)*exp(-exp(1/x)-x^2+x+5)/x^2,x, algorithm="fricas")

[Out]

e^(-x^2 + x - e^(1/x) + 5)

________________________________________________________________________________________

giac [A]  time = 0.16, size = 15, normalized size = 0.88 \begin {gather*} e^{\left (-x^{2} + x - e^{\frac {1}{x}} + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(1/x)-2*x^3+x^2)*exp(-exp(1/x)-x^2+x+5)/x^2,x, algorithm="giac")

[Out]

e^(-x^2 + x - e^(1/x) + 5)

________________________________________________________________________________________

maple [A]  time = 0.17, size = 16, normalized size = 0.94

method	result	size
norman	\({\mathrm e}^{-{\mathrm e}^{\frac {1}{x}}-x^{2}+x +5}\)	\(16\)
risch	\({\mathrm e}^{-{\mathrm e}^{\frac {1}{x}}-x^{2}+x +5}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(1/x)-2*x^3+x^2)*exp(-exp(1/x)-x^2+x+5)/x^2,x,method=_RETURNVERBOSE)

[Out]

exp(-exp(1/x)-x^2+x+5)

________________________________________________________________________________________

maxima [A]  time = 0.49, size = 15, normalized size = 0.88 \begin {gather*} e^{\left (-x^{2} + x - e^{\frac {1}{x}} + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(1/x)-2*x^3+x^2)*exp(-exp(1/x)-x^2+x+5)/x^2,x, algorithm="maxima")

[Out]

e^(-x^2 + x - e^(1/x) + 5)

________________________________________________________________________________________

mupad [B]  time = 1.79, size = 18, normalized size = 1.06 \begin {gather*} {\mathrm {e}}^{-{\mathrm {e}}^{1/x}}\,{\mathrm {e}}^5\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x - exp(1/x) - x^2 + 5)*(exp(1/x) + x^2 - 2*x^3))/x^2,x)

[Out]

exp(-exp(1/x))*exp(5)*exp(-x^2)*exp(x)

________________________________________________________________________________________

sympy [A]  time = 0.28, size = 12, normalized size = 0.71 \begin {gather*} e^{- x^{2} + x - e^{\frac {1}{x}} + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(1/x)-2*x**3+x**2)*exp(-exp(1/x)-x**2+x+5)/x**2,x)

[Out]

exp(-x**2 + x - exp(1/x) + 5)

________________________________________________________________________________________