Solving Integral of cos^2*sqrt(u)

[Punkyc7]

Homework Statement

integral of cos^2 * (sqr(1+tan^2))

Homework Equations

The Attempt at a Solution

let u = 1 +tan^2
du = sec^2

im not sure how 1/cos^2 gets accounted for the cos^2 in the front

 

[hunt_mat]

You did your differentiation wrong. In fact you don't need to use substitution. Firstly what is 1+tan^{2}x?

 

[Mark44]

Homework Statement

integral of cos^2 * (sqr(1+tan^2))

Homework Equations

The Attempt at a Solution

let u = 1 +tan^2
du = sec^2

If u = 1 + tan^2(theta), du = 2tan(theta)*sec^2(theta)d(theta)

In any case, this is not a good substitution to use.

There are some trig identities that can be used to simplify the integrand first, and then the integration is very simple.

im not sure how 1/cos^2 gets accounted for the cos^2 in the front