How do you integrate #int 1/(sqrtx(1+x))# by trigonometric substitution?
1 Answer
Sep 11, 2016
Explanation:
We have the integral:
#intdx/(sqrtx(1+x))#
We will use the substitution
#=2intdx/(2sqrtx(1+x))=2int(sec^2thetad theta)/(1+tan^2theta)#
Through the Pythagorean identity,
#=2intsec^2theta/sec^2thetad theta=2intd theta=2theta+C#
From
#=2arctan(sqrtx)+C#