Question Number 2770 by Yozzi last updated on 26/Nov/15

∫_2 ^∞ (dx/(x(√(x−1))))=?

Answered by prakash jain last updated on 27/Nov/15

x−1=tan^2 u dx=2tan usec^2 udu x=sec^2 u ∫(dx/(x(√(x−1))))=∫ ((2tan usec^2 u)/(sec^2 utan u))du=∫2du=2u =2tan^(−1) ((√(x−1))) limits =2[(π/2)−(π/4)]=(π/2)