3.102.93 \(\int e^{-e^{1+e^{32}-2 x+x^2+e^{16} (-2+2 x)}} (-3 x+e^{1+e^{32}-2 x+x^2+e^{16} (-2+2 x)} (-4 x^2+4 e^{16} x^2+4 x^3)+(2 x+e^{1+e^{32}-2 x+x^2+e^{16} (-2+2 x)} (2 x^2-2 e^{16} x^2-2 x^3)) \log (x)) \, dx\)

Optimal. Leaf size=22 \[ e^{-e^{\left (-1+e^{16}+x\right )^2}} x^2 (-2+\log (x)) \]

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Rubi [F]  time = 15.73, 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^{1+e^{32}-2 x+x^2+e^{16} (-2+2 x)}} \left (-3 x+e^{1+e^{32}-2 x+x^2+e^{16} (-2+2 x)} \left (-4 x^2+4 e^{16} x^2+4 x^3\right )+\left (2 x+e^{1+e^{32}-2 x+x^2+e^{16} (-2+2 x)} \left (2 x^2-2 e^{16} x^2-2 x^3\right )\right ) \log (x)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-3*x + E^(1 + E^32 - 2*x + x^2 + E^16*(-2 + 2*x))*(-4*x^2 + 4*E^16*x^2 + 4*x^3) + (2*x + E^(1 + E^32 - 2*
x + x^2 + E^16*(-2 + 2*x))*(2*x^2 - 2*E^16*x^2 - 2*x^3))*Log[x])/E^E^(1 + E^32 - 2*x + x^2 + E^16*(-2 + 2*x)),
x]

[Out]

-3*Defer[Int][x/E^E^((-1 + E^16)^2 - 2*(1 - E^16)*x + x^2), x] + 2*Log[x]*Defer[Int][x/E^E^((-1 + E^16)^2 - 2*
(1 - E^16)*x + x^2), x] - 4*(1 - E^16)*Defer[Int][E^(E^32 - E^(-1 + E^16 + x)^2 + 2*E^16*(-1 + x) + (-1 + x)^2
)*x^2, x] + 2*(1 - E^16)*Log[x]*Defer[Int][E^(E^32 - E^(-1 + E^16 + x)^2 + 2*E^16*(-1 + x) + (-1 + x)^2)*x^2,
x] + 4*Defer[Int][E^(E^32 - E^(-1 + E^16 + x)^2 + 2*E^16*(-1 + x) + (-1 + x)^2)*x^3, x] - 2*Log[x]*Defer[Int][
E^(E^32 - E^(-1 + E^16 + x)^2 + 2*E^16*(-1 + x) + (-1 + x)^2)*x^3, x] - 2*Defer[Int][Defer[Int][x/E^E^((-1 + E
^16)^2 - 2*(1 - E^16)*x + x^2), x]/x, x] - 2*(1 - E^16)*Defer[Int][Defer[Int][E^(E^32 - E^(-1 + E^16 + x)^2 +
2*E^16*(-1 + x) + (-1 + x)^2)*x^2, x]/x, x] + 2*Defer[Int][Defer[Int][E^(E^32 - E^(-1 + E^16 + x)^2 + 2*E^16*(
-1 + x) + (-1 + x)^2)*x^3, x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \left (-3+4 e^{\left (-1+e^{16}+x\right )^2} x \left (-1+e^{16}+x\right )+2 \left (1-e^{\left (-1+e^{16}+x\right )^2} x \left (-1+e^{16}+x\right )\right ) \log (x)\right ) \, dx\\ &=\int \left (2 \exp \left (-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}+\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2\right ) \left (1-e^{16}-x\right ) x^2 (-2+\log (x))+e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x (-3+2 \log (x))\right ) \, dx\\ &=2 \int \exp \left (-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}+\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2\right ) \left (1-e^{16}-x\right ) x^2 (-2+\log (x)) \, dx+\int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x (-3+2 \log (x)) \, dx\\ &=2 \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) \left (1-e^{16}-x\right ) x^2 (-2+\log (x)) \, dx+\int \left (-3 e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x+2 e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \log (x)\right ) \, dx\\ &=2 \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \log (x) \, dx+2 \int \left (2 \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \left (-1+e^{16}+x\right )-\exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \left (-1+e^{16}+x\right ) \log (x)\right ) \, dx-3 \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx\\ &=-\left (2 \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \left (-1+e^{16}+x\right ) \log (x) \, dx\right )-2 \int \frac {\int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx}{x} \, dx-3 \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx+4 \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \left (-1+e^{16}+x\right ) \, dx+(2 \log (x)) \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx\\ &=-\left (2 \int \frac {\int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx}{x} \, dx\right )+2 \int \frac {\left (-1+e^{16}\right ) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx+\int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx}{x} \, dx-3 \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx+4 \int \left (\exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) \left (-1+e^{16}\right ) x^2+\exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3\right ) \, dx+(2 \log (x)) \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx-(2 \log (x)) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx+\left (2 \left (1-e^{16}\right ) \log (x)\right ) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx\\ &=-\left (2 \int \frac {\int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx}{x} \, dx\right )+2 \int \left (\frac {(-1+e) (1+e) \left (1+e^2\right ) \left (1+e^4\right ) \left (1+e^8\right ) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx}{x}+\frac {\int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx}{x}\right ) \, dx-3 \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx+4 \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx-\left (4 \left (1-e^{16}\right )\right ) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx+(2 \log (x)) \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx-(2 \log (x)) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx+\left (2 \left (1-e^{16}\right ) \log (x)\right ) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx\\ &=-\left (2 \int \frac {\int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx}{x} \, dx\right )+2 \int \frac {\int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx}{x} \, dx-3 \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx+4 \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx-\left (2 \left (1-e^{16}\right )\right ) \int \frac {\int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx}{x} \, dx-\left (4 \left (1-e^{16}\right )\right ) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx+(2 \log (x)) \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx-(2 \log (x)) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx+\left (2 \left (1-e^{16}\right ) \log (x)\right ) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 4.19, size = 22, normalized size = 1.00 \begin {gather*} e^{-e^{\left (-1+e^{16}+x\right )^2}} x^2 (-2+\log (x)) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-3*x + E^(1 + E^32 - 2*x + x^2 + E^16*(-2 + 2*x))*(-4*x^2 + 4*E^16*x^2 + 4*x^3) + (2*x + E^(1 + E^3
2 - 2*x + x^2 + E^16*(-2 + 2*x))*(2*x^2 - 2*E^16*x^2 - 2*x^3))*Log[x])/E^E^(1 + E^32 - 2*x + x^2 + E^16*(-2 +
2*x)),x]

[Out]

(x^2*(-2 + Log[x]))/E^E^(-1 + E^16 + x)^2

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fricas [A]  time = 1.13, size = 34, normalized size = 1.55 \begin {gather*} {\left (x^{2} \log \relax (x) - 2 \, x^{2}\right )} e^{\left (-e^{\left (x^{2} + 2 \, {\left (x - 1\right )} e^{16} - 2 \, x + e^{32} + 1\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^2*exp(16)-2*x^3+2*x^2)*exp(exp(16)^2+(2*x-2)*exp(16)+x^2-2*x+1)+2*x)*log(x)+(4*x^2*exp(16)+4
*x^3-4*x^2)*exp(exp(16)^2+(2*x-2)*exp(16)+x^2-2*x+1)-3*x)/exp(exp(exp(16)^2+(2*x-2)*exp(16)+x^2-2*x+1)),x, alg
orithm="fricas")

[Out]

(x^2*log(x) - 2*x^2)*e^(-e^(x^2 + 2*(x - 1)*e^16 - 2*x + e^32 + 1))

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giac [B]  time = 0.36, size = 121, normalized size = 5.50 \begin {gather*} {\left (x^{2} e^{\left (x^{2} + 2 \, x e^{16} - 2 \, x + e^{32} - 2 \, e^{16} - e^{\left (x^{2} + 2 \, x e^{16} - 2 \, x + e^{32} - 2 \, e^{16} + 1\right )} + 1\right )} \log \relax (x) - 2 \, x^{2} e^{\left (x^{2} + 2 \, x e^{16} - 2 \, x + e^{32} - 2 \, e^{16} - e^{\left (x^{2} + 2 \, x e^{16} - 2 \, x + e^{32} - 2 \, e^{16} + 1\right )} + 1\right )}\right )} e^{\left (-x^{2} - 2 \, x e^{16} + 2 \, x - e^{32} + 2 \, e^{16} - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^2*exp(16)-2*x^3+2*x^2)*exp(exp(16)^2+(2*x-2)*exp(16)+x^2-2*x+1)+2*x)*log(x)+(4*x^2*exp(16)+4
*x^3-4*x^2)*exp(exp(16)^2+(2*x-2)*exp(16)+x^2-2*x+1)-3*x)/exp(exp(exp(16)^2+(2*x-2)*exp(16)+x^2-2*x+1)),x, alg
orithm="giac")

[Out]

(x^2*e^(x^2 + 2*x*e^16 - 2*x + e^32 - 2*e^16 - e^(x^2 + 2*x*e^16 - 2*x + e^32 - 2*e^16 + 1) + 1)*log(x) - 2*x^
2*e^(x^2 + 2*x*e^16 - 2*x + e^32 - 2*e^16 - e^(x^2 + 2*x*e^16 - 2*x + e^32 - 2*e^16 + 1) + 1))*e^(-x^2 - 2*x*e
^16 + 2*x - e^32 + 2*e^16 - 1)

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maple [A]  time = 0.18, size = 32, normalized size = 1.45

method	result	size
risch	\(\left (\ln \relax (x )-2\right ) x^{2} {\mathrm e}^{-{\mathrm e}^{2 x \,{\mathrm e}^{16}+x^{2}-2 \,{\mathrm e}^{16}+{\mathrm e}^{32}-2 x +1}}\)	\(32\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-2*x^2*exp(16)-2*x^3+2*x^2)*exp(exp(16)^2+(2*x-2)*exp(16)+x^2-2*x+1)+2*x)*ln(x)+(4*x^2*exp(16)+4*x^3-4*
x^2)*exp(exp(16)^2+(2*x-2)*exp(16)+x^2-2*x+1)-3*x)/exp(exp(exp(16)^2+(2*x-2)*exp(16)+x^2-2*x+1)),x,method=_RET
URNVERBOSE)

[Out]

(ln(x)-2)*x^2*exp(-exp(2*x*exp(16)+x^2-2*exp(16)+exp(32)-2*x+1))

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maxima [A]  time = 1.06, size = 36, normalized size = 1.64 \begin {gather*} {\left (x^{2} \log \relax (x) - 2 \, x^{2}\right )} e^{\left (-e^{\left (x^{2} + 2 \, x e^{16} - 2 \, x + e^{32} - 2 \, e^{16} + 1\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^2*exp(16)-2*x^3+2*x^2)*exp(exp(16)^2+(2*x-2)*exp(16)+x^2-2*x+1)+2*x)*log(x)+(4*x^2*exp(16)+4
*x^3-4*x^2)*exp(exp(16)^2+(2*x-2)*exp(16)+x^2-2*x+1)-3*x)/exp(exp(exp(16)^2+(2*x-2)*exp(16)+x^2-2*x+1)),x, alg
orithm="maxima")

[Out]

(x^2*log(x) - 2*x^2)*e^(-e^(x^2 + 2*x*e^16 - 2*x + e^32 - 2*e^16 + 1))

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mupad [B]  time = 7.72, size = 35, normalized size = 1.59 \begin {gather*} x^2\,{\mathrm {e}}^{-{\mathrm {e}}^{-2\,{\mathrm {e}}^{16}}\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{x^2}\,\mathrm {e}\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^{16}}\,{\mathrm {e}}^{{\mathrm {e}}^{32}}}\,\left (\ln \relax (x)-2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-exp(exp(32) - 2*x + x^2 + exp(16)*(2*x - 2) + 1))*(log(x)*(2*x - exp(exp(32) - 2*x + x^2 + exp(16)*(2
*x - 2) + 1)*(2*x^2*exp(16) - 2*x^2 + 2*x^3)) - 3*x + exp(exp(32) - 2*x + x^2 + exp(16)*(2*x - 2) + 1)*(4*x^2*
exp(16) - 4*x^2 + 4*x^3)),x)

[Out]

x^2*exp(-exp(-2*exp(16))*exp(-2*x)*exp(x^2)*exp(1)*exp(2*x*exp(16))*exp(exp(32)))*(log(x) - 2)

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sympy [A]  time = 49.25, size = 34, normalized size = 1.55 \begin {gather*} \left (x^{2} \log {\relax (x )} - 2 x^{2}\right ) e^{- e^{x^{2} - 2 x + \left (2 x - 2\right ) e^{16} + 1 + e^{32}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x**2*exp(16)-2*x**3+2*x**2)*exp(exp(16)**2+(2*x-2)*exp(16)+x**2-2*x+1)+2*x)*ln(x)+(4*x**2*exp(
16)+4*x**3-4*x**2)*exp(exp(16)**2+(2*x-2)*exp(16)+x**2-2*x+1)-3*x)/exp(exp(exp(16)**2+(2*x-2)*exp(16)+x**2-2*x
+1)),x)

[Out]

(x**2*log(x) - 2*x**2)*exp(-exp(x**2 - 2*x + (2*x - 2)*exp(16) + 1 + exp(32)))

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