I got it !!

it will = sec^-1 [ln t + 1] + C

Solving by :

Sqrt( u . (u+2) )

= sqrt [ (u+0) . (u+1+1) ]

= sqrt [ (u+1-1) . (u+1+1) ]

then i will mulitplyed the brackets

it will be = sqrt [ (u+1)^2 - 1 ]

put k = u+1

dk = du

it will be k . Sqrt(k^2 -1)

Trigonometric substitution k = sec θ

... etc

Right ??

One question : it allowed to multiply the brackets in BLUE making u+1 as an one thing??

i hope u will understand what i mean !

Again: Sorry for bad english