Definite integral: dx/(1+(cos(x))^2) (0<=x<=π/4)

[Pam_pam]

Hello, i have problem with this integral dx/(1+(cos(x))^2) (0<=x<=π/4).
I tried to solve it by multiplying its nominator and denominator by (sin(x))^2, but i could not find what substitute to assign as u and so du. I will be grateful if someone​ show me the starting point frow where i will be able to solve this integral.

 

[Deleted member 4993]

Hello, i have problem with this integral dx/(1+(cos(x))^2) (0<=x<=π/4).
I tried to solve it by multiplying its nominator and denominator by (sin(x))^2, but i could not find what substitute to assign as u and so du. I will be grateful if someone​ show me the starting point frow where i will be able to solve this integral.

Substitute

dx/[1 + cos²(x)] = sec²(x)/[1 + sec²(x)] dx = sec²(x)/[2 + tan²(x)] dx

Now substitute:

u = tan(x) → du = sec²(x) dx

and continue.....