Question

integration of 1/(root x +sqrtx^2)

Answer 1

Hey Dear, The answer ☺ to this is : By inspection rather than trig substitution.

Explanation:

Notice that the x in the top is proportional to the derivative of the function under the square root. So just write down (x2+1)−12+1 as a trial (rather like integrating any power of x) and differentiate it. By the chain rule, the function under the square root will provide the 2x and the 2's will cancel, so the trial was an immediate success.

hope it helped (^^)