Question

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

Answer 1

u = e^x
du/dx = e^x
du = e^xdx
the integral becomes :
du/(u^2 + 3)
with boundaries 1 to infinity since e^0 = 1.
the solution for this integral will be
(1/(3^0.5)) * arctan(u/(3^0.5))

if you plug the boundaries you will get:
(1/(3^0.5)) * (90 - 30) = 60/(3^0.5)

hopefully i'm right lol

Answer 2

.6046

Answer 3

pi/(3 sqrt(3))=.6046

Answer 4

integral (e^x)/((e^2x)+3) from 0 to infinity
u = e^x +3
du = e^x dx
= e^xdx the integral becomes
=integral du/u from o to infinity
= lnu] from 0 to infinity
= ln(e^x +3)]from 0 to infinity

Answer 5

so what is that value ? is it converges or divereges ?

Answer 6

if im right its converges

Answer 7

=0.6046 converge

Answer 8

yep in radians

Answer 9

so what is that value ? is it converges or divereges ?

Answer 10

i think the u subst is wrong, becuz is e^2x