Evaluate the indefinite integral. (use c for the constant of integration.) sin(2x) 24 + cos2(x) dx

Using substitution, the result of the integral is given by:

We want to calculate the following integral:

The following identity is used to simplify the cosine squared:

Replacing into the integral:

The substitution is:

Hence:

Since , the result as a function of x is:

A similar problem is given at link

Possibly you refer to the integral,

Recall the double angle identity,

Then the integral is equivalent to

Let so that . Then the integral becomes

We can rewrite this to try to get it in a form that more resembles the original integrand.

where the constant term got absorbed into the general constant .

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2