3.5.45 \(\int \frac {e^{\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} (-e^{x^2}+x)}{-10+e^{\frac {e^x}{2 x}}-x}} (220 x+40 x^2+2 x^3+e^{\frac {e^x}{x}} (2 x-4 e^{x^2} x^2)+e^{x^2} (-400 x^2-80 x^3-4 x^4)+e^{\frac {e^x}{2 x}} (e^x (-1+x)-42 x-4 x^2+e^{x^2} (80 x^2+8 x^3)))}{200 x+2 e^{\frac {e^x}{x}} x+40 x^2+2 x^3+e^{\frac {e^x}{2 x}} (-40 x-4 x^2)} \, dx\)

Optimal. Leaf size=32 \[ e^{-e^{x^2}+x+\frac {x}{10-e^{\frac {e^x}{2 x}}+x}} \]

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Rubi [F]  time = 105.93, 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 \frac {\exp \left (\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right ) \left (220 x+40 x^2+2 x^3+e^{\frac {e^x}{x}} \left (2 x-4 e^{x^2} x^2\right )+e^{x^2} \left (-400 x^2-80 x^3-4 x^4\right )+e^{\frac {e^x}{2 x}} \left (e^x (-1+x)-42 x-4 x^2+e^{x^2} \left (80 x^2+8 x^3\right )\right )\right )}{200 x+2 e^{\frac {e^x}{x}} x+40 x^2+2 x^3+e^{\frac {e^x}{2 x}} \left (-40 x-4 x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((-11*x - x^2 + E^x^2*(10 + x) + E^(E^x/(2*x))*(-E^x^2 + x))/(-10 + E^(E^x/(2*x)) - x))*(220*x + 40*x^2
+ 2*x^3 + E^(E^x/x)*(2*x - 4*E^x^2*x^2) + E^x^2*(-400*x^2 - 80*x^3 - 4*x^4) + E^(E^x/(2*x))*(E^x*(-1 + x) - 4
2*x - 4*x^2 + E^x^2*(80*x^2 + 8*x^3))))/(200*x + 2*E^(E^x/x)*x + 40*x^2 + 2*x^3 + E^(E^x/(2*x))*(-40*x - 4*x^2
)),x]

[Out]

110*Defer[Int][E^((-11*x - x^2 + E^x^2*(10 + x) + E^(E^x/(2*x))*(-E^x^2 + x))/(-10 + E^(E^x/(2*x)) - x))/(-10
+ E^(E^x/(2*x)) - x)^2, x] - 21*Defer[Int][E^(E^x/(2*x) + (-11*x - x^2 + E^x^2*(10 + x) + E^(E^x/(2*x))*(-E^x^
2 + x))/(-10 + E^(E^x/(2*x)) - x))/(-10 + E^(E^x/(2*x)) - x)^2, x] + Defer[Int][E^(E^x/x + (-11*x - x^2 + E^x^
2*(10 + x) + E^(E^x/(2*x))*(-E^x^2 + x))/(-10 + E^(E^x/(2*x)) - x))/(-10 + E^(E^x/(2*x)) - x)^2, x] + Defer[In
t][E^(E^x/(2*x) + x + (-11*x - x^2 + E^x^2*(10 + x) + E^(E^x/(2*x))*(-E^x^2 + x))/(-10 + E^(E^x/(2*x)) - x))/(
-10 + E^(E^x/(2*x)) - x)^2, x]/2 - 2*Defer[Int][E^(x^2 + (-11*x - x^2 + E^x^2*(10 + x) + E^(E^x/(2*x))*(-E^x^2
+ x))/(-10 + E^(E^x/(2*x)) - x))*x, x] + 20*Defer[Int][(E^((-11*x - x^2 + E^x^2*(10 + x) + E^(E^x/(2*x))*(-E^
x^2 + x))/(-10 + E^(E^x/(2*x)) - x))*x)/(-10 + E^(E^x/(2*x)) - x)^2, x] - 2*Defer[Int][(E^(E^x/(2*x) + (-11*x
- x^2 + E^x^2*(10 + x) + E^(E^x/(2*x))*(-E^x^2 + x))/(-10 + E^(E^x/(2*x)) - x))*x)/(-10 + E^(E^x/(2*x)) - x)^2
, x] + Defer[Int][(E^((-11*x - x^2 + E^x^2*(10 + x) + E^(E^x/(2*x))*(-E^x^2 + x))/(-10 + E^(E^x/(2*x)) - x))*x
^2)/(-10 + E^(E^x/(2*x)) - x)^2, x] - Defer[Int][E^(E^x/(2*x) + x + (-11*x - x^2 + E^x^2*(10 + x) + E^(E^x/(2*
x))*(-E^x^2 + x))/(-10 + E^(E^x/(2*x)) - x))/(x*(10 - E^(E^x/(2*x)) + x)^2), x]/2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right ) \left (220 x+40 x^2+2 x^3+e^{\frac {e^x}{x}} \left (2 x-4 e^{x^2} x^2\right )+e^{x^2} \left (-400 x^2-80 x^3-4 x^4\right )+e^{\frac {e^x}{2 x}} \left (e^x (-1+x)-42 x-4 x^2+e^{x^2} \left (80 x^2+8 x^3\right )\right )\right )}{2 x \left (10-e^{\frac {e^x}{2 x}}+x\right )^2} \, dx\\ &=\frac {1}{2} \int \frac {\exp \left (\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right ) \left (220 x+40 x^2+2 x^3+e^{\frac {e^x}{x}} \left (2 x-4 e^{x^2} x^2\right )+e^{x^2} \left (-400 x^2-80 x^3-4 x^4\right )+e^{\frac {e^x}{2 x}} \left (e^x (-1+x)-42 x-4 x^2+e^{x^2} \left (80 x^2+8 x^3\right )\right )\right )}{x \left (10-e^{\frac {e^x}{2 x}}+x\right )^2} \, dx\\ &=\frac {1}{2} \int \left (\frac {220 \exp \left (\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right )}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2}-\frac {42 \exp \left (\frac {e^x}{2 x}+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right )}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2}+\frac {2 \exp \left (\frac {e^x}{x}+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right )}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2}+\frac {\exp \left (\frac {e^x}{2 x}+x+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right ) (-1+x)}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2 x}-4 \exp \left (x^2+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right ) x+\frac {40 \exp \left (\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right ) x}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2}-\frac {4 \exp \left (\frac {e^x}{2 x}+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right ) x}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2}+\frac {2 \exp \left (\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right ) x^2}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2}\right ) \, dx\\ &=\frac {1}{2} \int \frac {\exp \left (\frac {e^x}{2 x}+x+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right ) (-1+x)}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2 x} \, dx-2 \int \exp \left (x^2+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right ) x \, dx-2 \int \frac {\exp \left (\frac {e^x}{2 x}+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right ) x}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx+20 \int \frac {\exp \left (\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right ) x}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx-21 \int \frac {\exp \left (\frac {e^x}{2 x}+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right )}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx+110 \int \frac {\exp \left (\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right )}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx+\int \frac {\exp \left (\frac {e^x}{x}+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right )}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx+\int \frac {\exp \left (\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}\right ) x^2}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx\\ &=\frac {1}{2} \int \left (\frac {e^{\frac {e^x}{2 x}+x+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}}}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2}-\frac {e^{\frac {e^x}{2 x}+x+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}}}{x \left (10-e^{\frac {e^x}{2 x}}+x\right )^2}\right ) \, dx-2 \int e^{x^2+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}} x \, dx-2 \int \frac {e^{\frac {e^x}{2 x}+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}} x}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx+20 \int \frac {e^{\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}} x}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx-21 \int \frac {e^{\frac {e^x}{2 x}+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}}}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx+110 \int \frac {e^{\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}}}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx+\int \frac {e^{\frac {e^x}{x}+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}}}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx+\int \frac {e^{\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}} x^2}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx\\ &=\frac {1}{2} \int \frac {e^{\frac {e^x}{2 x}+x+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}}}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx-\frac {1}{2} \int \frac {e^{\frac {e^x}{2 x}+x+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}}}{x \left (10-e^{\frac {e^x}{2 x}}+x\right )^2} \, dx-2 \int e^{x^2+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}} x \, dx-2 \int \frac {e^{\frac {e^x}{2 x}+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}} x}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx+20 \int \frac {e^{\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}} x}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx-21 \int \frac {e^{\frac {e^x}{2 x}+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}}}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx+110 \int \frac {e^{\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}}}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx+\int \frac {e^{\frac {e^x}{x}+\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}}}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx+\int \frac {e^{\frac {-11 x-x^2+e^{x^2} (10+x)+e^{\frac {e^x}{2 x}} \left (-e^{x^2}+x\right )}{-10+e^{\frac {e^x}{2 x}}-x}} x^2}{\left (-10+e^{\frac {e^x}{2 x}}-x\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.46, size = 33, normalized size = 1.03 \begin {gather*} e^{-e^{x^2}+x-\frac {x}{-10+e^{\frac {e^x}{2 x}}-x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((-11*x - x^2 + E^x^2*(10 + x) + E^(E^x/(2*x))*(-E^x^2 + x))/(-10 + E^(E^x/(2*x)) - x))*(220*x +
40*x^2 + 2*x^3 + E^(E^x/x)*(2*x - 4*E^x^2*x^2) + E^x^2*(-400*x^2 - 80*x^3 - 4*x^4) + E^(E^x/(2*x))*(E^x*(-1 +
x) - 42*x - 4*x^2 + E^x^2*(80*x^2 + 8*x^3))))/(200*x + 2*E^(E^x/x)*x + 40*x^2 + 2*x^3 + E^(E^x/(2*x))*(-40*x -
4*x^2)),x]

[Out]

E^(-E^x^2 + x - x/(-10 + E^(E^x/(2*x)) - x))

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fricas [A]  time = 0.77, size = 51, normalized size = 1.59 \begin {gather*} e^{\left (\frac {x^{2} - {\left (x + 10\right )} e^{\left (x^{2}\right )} - {\left (x - e^{\left (x^{2}\right )}\right )} e^{\left (\frac {e^{x}}{2 \, x}\right )} + 11 \, x}{x - e^{\left (\frac {e^{x}}{2 \, x}\right )} + 10}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^2*exp(x^2)+2*x)*exp(1/2*exp(x)/x)^2+((8*x^3+80*x^2)*exp(x^2)+(x-1)*exp(x)-4*x^2-42*x)*exp(1/2
*exp(x)/x)+(-4*x^4-80*x^3-400*x^2)*exp(x^2)+2*x^3+40*x^2+220*x)*exp(((-exp(x^2)+x)*exp(1/2*exp(x)/x)+(x+10)*ex
p(x^2)-x^2-11*x)/(exp(1/2*exp(x)/x)-x-10))/(2*x*exp(1/2*exp(x)/x)^2+(-4*x^2-40*x)*exp(1/2*exp(x)/x)+2*x^3+40*x
^2+200*x),x, algorithm="fricas")

[Out]

e^((x^2 - (x + 10)*e^(x^2) - (x - e^(x^2))*e^(1/2*e^x/x) + 11*x)/(x - e^(1/2*e^x/x) + 10))

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giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^2*exp(x^2)+2*x)*exp(1/2*exp(x)/x)^2+((8*x^3+80*x^2)*exp(x^2)+(x-1)*exp(x)-4*x^2-42*x)*exp(1/2
*exp(x)/x)+(-4*x^4-80*x^3-400*x^2)*exp(x^2)+2*x^3+40*x^2+220*x)*exp(((-exp(x^2)+x)*exp(1/2*exp(x)/x)+(x+10)*ex
p(x^2)-x^2-11*x)/(exp(1/2*exp(x)/x)-x-10))/(2*x*exp(1/2*exp(x)/x)^2+(-4*x^2-40*x)*exp(1/2*exp(x)/x)+2*x^3+40*x
^2+200*x),x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Evaluation time: 3.12Unable to divide, perhaps due to rounding error%%%{-32,[0,8,9,6,25]%%%}+%%%{-1696,[0,8
,9,6,24]%%%

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maple [B]  time = 0.34, size = 63, normalized size = 1.97

method	result	size
risch	\({\mathrm e}^{\frac {{\mathrm e}^{\frac {2 x^{3}+{\mathrm e}^{x}}{2 x}}-{\mathrm e}^{x^{2}} x -{\mathrm e}^{\frac {{\mathrm e}^{x}}{2 x}} x +x^{2}-10 \,{\mathrm e}^{x^{2}}+11 x}{x -{\mathrm e}^{\frac {{\mathrm e}^{x}}{2 x}}+10}}\)	\(63\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-4*x^2*exp(x^2)+2*x)*exp(1/2*exp(x)/x)^2+((8*x^3+80*x^2)*exp(x^2)+(x-1)*exp(x)-4*x^2-42*x)*exp(1/2*exp(x
)/x)+(-4*x^4-80*x^3-400*x^2)*exp(x^2)+2*x^3+40*x^2+220*x)*exp(((-exp(x^2)+x)*exp(1/2*exp(x)/x)+(x+10)*exp(x^2)
-x^2-11*x)/(exp(1/2*exp(x)/x)-x-10))/(2*x*exp(1/2*exp(x)/x)^2+(-4*x^2-40*x)*exp(1/2*exp(x)/x)+2*x^3+40*x^2+200
*x),x,method=_RETURNVERBOSE)

[Out]

exp((exp(1/2*(2*x^3+exp(x))/x)-exp(x^2)*x-exp(1/2*exp(x)/x)*x+x^2-10*exp(x^2)+11*x)/(x-exp(1/2*exp(x)/x)+10))

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {1}{2} \, \int \frac {{\left (2 \, x^{3} + 40 \, x^{2} - 4 \, {\left (x^{4} + 20 \, x^{3} + 100 \, x^{2}\right )} e^{\left (x^{2}\right )} - 2 \, {\left (2 \, x^{2} e^{\left (x^{2}\right )} - x\right )} e^{\left (\frac {e^{x}}{x}\right )} - {\left (4 \, x^{2} - 8 \, {\left (x^{3} + 10 \, x^{2}\right )} e^{\left (x^{2}\right )} - {\left (x - 1\right )} e^{x} + 42 \, x\right )} e^{\left (\frac {e^{x}}{2 \, x}\right )} + 220 \, x\right )} e^{\left (\frac {x^{2} - {\left (x + 10\right )} e^{\left (x^{2}\right )} - {\left (x - e^{\left (x^{2}\right )}\right )} e^{\left (\frac {e^{x}}{2 \, x}\right )} + 11 \, x}{x - e^{\left (\frac {e^{x}}{2 \, x}\right )} + 10}\right )}}{x^{3} + 20 \, x^{2} + x e^{\left (\frac {e^{x}}{x}\right )} - 2 \, {\left (x^{2} + 10 \, x\right )} e^{\left (\frac {e^{x}}{2 \, x}\right )} + 100 \, x}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^2*exp(x^2)+2*x)*exp(1/2*exp(x)/x)^2+((8*x^3+80*x^2)*exp(x^2)+(x-1)*exp(x)-4*x^2-42*x)*exp(1/2
*exp(x)/x)+(-4*x^4-80*x^3-400*x^2)*exp(x^2)+2*x^3+40*x^2+220*x)*exp(((-exp(x^2)+x)*exp(1/2*exp(x)/x)+(x+10)*ex
p(x^2)-x^2-11*x)/(exp(1/2*exp(x)/x)-x-10))/(2*x*exp(1/2*exp(x)/x)^2+(-4*x^2-40*x)*exp(1/2*exp(x)/x)+2*x^3+40*x
^2+200*x),x, algorithm="maxima")

[Out]

1/2*integrate((2*x^3 + 40*x^2 - 4*(x^4 + 20*x^3 + 100*x^2)*e^(x^2) - 2*(2*x^2*e^(x^2) - x)*e^(e^x/x) - (4*x^2
- 8*(x^3 + 10*x^2)*e^(x^2) - (x - 1)*e^x + 42*x)*e^(1/2*e^x/x) + 220*x)*e^((x^2 - (x + 10)*e^(x^2) - (x - e^(x
^2))*e^(1/2*e^x/x) + 11*x)/(x - e^(1/2*e^x/x) + 10))/(x^3 + 20*x^2 + x*e^(e^x/x) - 2*(x^2 + 10*x)*e^(1/2*e^x/x
) + 100*x), x)

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mupad [B]  time = 1.36, size = 141, normalized size = 4.41 \begin {gather*} {\mathrm {e}}^{-\frac {10\,{\mathrm {e}}^{x^2}}{x-{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{2\,x}}+10}}\,{\mathrm {e}}^{\frac {11\,x}{x-{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{2\,x}}+10}}\,{\mathrm {e}}^{-\frac {x\,{\mathrm {e}}^{x^2}}{x-{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{2\,x}}+10}}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{2\,x}}}{x-{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{2\,x}}+10}}\,{\mathrm {e}}^{\frac {x^2}{x-{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{2\,x}}+10}}\,{\mathrm {e}}^{-\frac {x\,{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{2\,x}}}{x-{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{2\,x}}+10}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((11*x - exp(exp(x)/(2*x))*(x - exp(x^2)) - exp(x^2)*(x + 10) + x^2)/(x - exp(exp(x)/(2*x)) + 10))*(22
0*x + exp(exp(x)/x)*(2*x - 4*x^2*exp(x^2)) - exp(x^2)*(400*x^2 + 80*x^3 + 4*x^4) - exp(exp(x)/(2*x))*(42*x - e
xp(x)*(x - 1) - exp(x^2)*(80*x^2 + 8*x^3) + 4*x^2) + 40*x^2 + 2*x^3))/(200*x - exp(exp(x)/(2*x))*(40*x + 4*x^2
) + 2*x*exp(exp(x)/x) + 40*x^2 + 2*x^3),x)

[Out]

exp(-(10*exp(x^2))/(x - exp(exp(x)/(2*x)) + 10))*exp((11*x)/(x - exp(exp(x)/(2*x)) + 10))*exp(-(x*exp(x^2))/(x
- exp(exp(x)/(2*x)) + 10))*exp((exp(x^2)*exp(exp(x)/(2*x)))/(x - exp(exp(x)/(2*x)) + 10))*exp(x^2/(x - exp(ex
p(x)/(2*x)) + 10))*exp(-(x*exp(exp(x)/(2*x)))/(x - exp(exp(x)/(2*x)) + 10))

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sympy [B]  time = 18.04, size = 42, normalized size = 1.31 \begin {gather*} e^{\frac {- x^{2} - 11 x + \left (x + 10\right ) e^{x^{2}} + \left (x - e^{x^{2}}\right ) e^{\frac {e^{x}}{2 x}}}{- x + e^{\frac {e^{x}}{2 x}} - 10}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x**2*exp(x**2)+2*x)*exp(1/2*exp(x)/x)**2+((8*x**3+80*x**2)*exp(x**2)+(x-1)*exp(x)-4*x**2-42*x)*
exp(1/2*exp(x)/x)+(-4*x**4-80*x**3-400*x**2)*exp(x**2)+2*x**3+40*x**2+220*x)*exp(((-exp(x**2)+x)*exp(1/2*exp(x
)/x)+(x+10)*exp(x**2)-x**2-11*x)/(exp(1/2*exp(x)/x)-x-10))/(2*x*exp(1/2*exp(x)/x)**2+(-4*x**2-40*x)*exp(1/2*ex
p(x)/x)+2*x**3+40*x**2+200*x),x)

[Out]

exp((-x**2 - 11*x + (x + 10)*exp(x**2) + (x - exp(x**2))*exp(exp(x)/(2*x)))/(-x + exp(exp(x)/(2*x)) - 10))

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