Question

How do I find `f(pi)` for `f(x)= 3 int_0^x cos(t)/cos(t/2)+cos(2t)/cos(t/2) dt` ?

Answer 1

`4*sin(3/2pi)`

Explanation:

Using that
`cos(t)+cos(2t)=2cos(t/2)cos(3/2t)`
so your indefinite integral is given by
`2int cos(3/2t)dt=4/3sin(3/2t)+C`
and our definite integral is given by
`4sin(3/2pi)`