3.26.41 \(\int e^{-e^{450 x^5-225 x^6}-x^2} (e^{e^{450 x^5-225 x^6}+x^2}-2 x+e^{450 x^5-225 x^6} (-2250 x^4+1350 x^5)) \, dx\)

Optimal. Leaf size=24 \[ e^{-e^{225 (2-x) x^5}-x^2}+x \]

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Rubi [F]  time = 1.93, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int e^{-e^{450 x^5-225 x^6}-x^2} \left (e^{e^{450 x^5-225 x^6}+x^2}-2 x+e^{450 x^5-225 x^6} \left (-2250 x^4+1350 x^5\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(-E^(450*x^5 - 225*x^6) - x^2)*(E^(E^(450*x^5 - 225*x^6) + x^2) - 2*x + E^(450*x^5 - 225*x^6)*(-2250*x^4
+ 1350*x^5)),x]

[Out]

x - 2*Defer[Int][E^(-E^(450*x^5 - 225*x^6) - x^2)*x, x] - 2250*Defer[Int][E^(-E^(450*x^5 - 225*x^6) - x^2 - 22
5*(-2 + x)*x^5)*x^4, x] + 1350*Defer[Int][E^(-E^(450*x^5 - 225*x^6) - x^2 - 225*(-2 + x)*x^5)*x^5, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^{e^{-225 (-2+x) x^5}-e^{450 x^5-225 x^6}}-2 e^{-e^{450 x^5-225 x^6}-x^2} x+450 e^{-e^{450 x^5-225 x^6}-x^2-225 (-2+x) x^5} x^4 (-5+3 x)\right ) \, dx\\ &=-\left (2 \int e^{-e^{450 x^5-225 x^6}-x^2} x \, dx\right )+450 \int e^{-e^{450 x^5-225 x^6}-x^2-225 (-2+x) x^5} x^4 (-5+3 x) \, dx+\int e^{e^{-225 (-2+x) x^5}-e^{450 x^5-225 x^6}} \, dx\\ &=-\left (2 \int e^{-e^{450 x^5-225 x^6}-x^2} x \, dx\right )+450 \int \left (-5 e^{-e^{450 x^5-225 x^6}-x^2-225 (-2+x) x^5} x^4+3 e^{-e^{450 x^5-225 x^6}-x^2-225 (-2+x) x^5} x^5\right ) \, dx+\int 1 \, dx\\ &=x-2 \int e^{-e^{450 x^5-225 x^6}-x^2} x \, dx+1350 \int e^{-e^{450 x^5-225 x^6}-x^2-225 (-2+x) x^5} x^5 \, dx-2250 \int e^{-e^{450 x^5-225 x^6}-x^2-225 (-2+x) x^5} x^4 \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.65, size = 22, normalized size = 0.92 \begin {gather*} e^{-e^{-225 (-2+x) x^5}-x^2}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-E^(450*x^5 - 225*x^6) - x^2)*(E^(E^(450*x^5 - 225*x^6) + x^2) - 2*x + E^(450*x^5 - 225*x^6)*(-22
50*x^4 + 1350*x^5)),x]

[Out]

E^(-E^(-225*(-2 + x)*x^5) - x^2) + x

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fricas [B]  time = 0.81, size = 43, normalized size = 1.79 \begin {gather*} {\left (x e^{\left (x^{2} + e^{\left (-225 \, x^{6} + 450 \, x^{5}\right )}\right )} + 1\right )} e^{\left (-x^{2} - e^{\left (-225 \, x^{6} + 450 \, x^{5}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(exp(-225*x^6+450*x^5)+x^2)+(1350*x^5-2250*x^4)*exp(-225*x^6+450*x^5)-2*x)/exp(exp(-225*x^6+450*
x^5)+x^2),x, algorithm="fricas")

[Out]

(x*e^(x^2 + e^(-225*x^6 + 450*x^5)) + 1)*e^(-x^2 - e^(-225*x^6 + 450*x^5))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int {\left (450 \, {\left (3 \, x^{5} - 5 \, x^{4}\right )} e^{\left (-225 \, x^{6} + 450 \, x^{5}\right )} - 2 \, x + e^{\left (x^{2} + e^{\left (-225 \, x^{6} + 450 \, x^{5}\right )}\right )}\right )} e^{\left (-x^{2} - e^{\left (-225 \, x^{6} + 450 \, x^{5}\right )}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(exp(-225*x^6+450*x^5)+x^2)+(1350*x^5-2250*x^4)*exp(-225*x^6+450*x^5)-2*x)/exp(exp(-225*x^6+450*
x^5)+x^2),x, algorithm="giac")

[Out]

integrate((450*(3*x^5 - 5*x^4)*e^(-225*x^6 + 450*x^5) - 2*x + e^(x^2 + e^(-225*x^6 + 450*x^5)))*e^(-x^2 - e^(-
225*x^6 + 450*x^5)), x)

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maple [A]  time = 0.05, size = 21, normalized size = 0.88

method	result	size
risch	\(x +{\mathrm e}^{-{\mathrm e}^{-225 x^{5} \left (x -2\right )}-x^{2}}\)	\(21\)
norman	\(\left (1+x \,{\mathrm e}^{{\mathrm e}^{-225 x^{6}+450 x^{5}}+x^{2}}\right ) {\mathrm e}^{-{\mathrm e}^{-225 x^{6}+450 x^{5}}-x^{2}}\)	\(42\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(-225*x^6+450*x^5)+x^2)+(1350*x^5-2250*x^4)*exp(-225*x^6+450*x^5)-2*x)/exp(exp(-225*x^6+450*x^5)+x
^2),x,method=_RETURNVERBOSE)

[Out]

x+exp(-exp(-225*x^5*(x-2))-x^2)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} x - \int 2 \, {\left (x e^{\left (225 \, x^{6}\right )} - 225 \, {\left (3 \, x^{5} - 5 \, x^{4}\right )} e^{\left (450 \, x^{5}\right )}\right )} e^{\left (-225 \, x^{6} - x^{2} - e^{\left (-225 \, x^{6} + 450 \, x^{5}\right )}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(exp(-225*x^6+450*x^5)+x^2)+(1350*x^5-2250*x^4)*exp(-225*x^6+450*x^5)-2*x)/exp(exp(-225*x^6+450*
x^5)+x^2),x, algorithm="maxima")

[Out]

x - integrate(2*(x*e^(225*x^6) - 225*(3*x^5 - 5*x^4)*e^(450*x^5))*e^(-225*x^6 - x^2 - e^(-225*x^6 + 450*x^5)),
x)

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mupad [B]  time = 1.63, size = 24, normalized size = 1.00 \begin {gather*} x+{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^{-{\mathrm {e}}^{-225\,x^6}\,{\mathrm {e}}^{450\,x^5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(- exp(450*x^5 - 225*x^6) - x^2)*(2*x - exp(exp(450*x^5 - 225*x^6) + x^2) + exp(450*x^5 - 225*x^6)*(22
50*x^4 - 1350*x^5)),x)

[Out]

x + exp(-x^2)*exp(-exp(-225*x^6)*exp(450*x^5))

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sympy [A]  time = 0.42, size = 19, normalized size = 0.79 \begin {gather*} x + e^{- x^{2} - e^{- 225 x^{6} + 450 x^{5}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(exp(-225*x**6+450*x**5)+x**2)+(1350*x**5-2250*x**4)*exp(-225*x**6+450*x**5)-2*x)/exp(exp(-225*x
**6+450*x**5)+x**2),x)

[Out]

x + exp(-x**2 - exp(-225*x**6 + 450*x**5))

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