Question

Evaluate the integral (e^x)/((e^2x)+3) from 0 to infinity

Answer 1

So, from our equation
u = e^x
du/dx = e^x du = e^xdxthe integral would be:

du/(u^2 + 3)

Using the boundaries 1 to infinity
As, e^0 = 1.the solution for this integral will be

(1/(3^0.5)) * arctan(u/(3^0.5))Plugging the boundaries

(1/(3^0.5)) * (90 - 30) = 60/(3^0.5)
=0.6046