What is int_-oo^oo (e^x)/((e^(2x))+3) dx?
1 Answer
Mar 24, 2016
Explanation:
Using trigonometric substitution
Since
So the expression becomes
=int_((-pi/2)^"+")^((pi/2)^"-") (sqrt3sec^2y)/(3tan^2y+3)dy=int_((-pi/2)^"+")^((pi/2)^"-") (sqrt3cancel(sec^2y))/(3cancel(sec^2y))dy
=(y/sqrt3)|_((-pi/2)^"+")^((pi/2)^"-")
=1/sqrt3[pi/2-(-pi/2)]=pi/sqrt3