The first step was your mistake.
So you're given
It would be better to set u equal to the denominator since the derivative of 1 is 0, allowing you to substitute more.
Set u as the denominator
Substitute Integrate Back track u Evaluate anti-derivative at limits Simplify
When you make substitution you must change the limits For example
u = 1+sin t
When t = 0 u = 1 and when t = pi/2 , u = 2
Thus the integral would be from 1 to 2, intgreal 1/u du
This will avoid some steps and would help in getting solutin early. in this case it would be simply log 2 since log 1 = 0