Question

(Sinx+cox)dx ?

Answer 1

`int(sinx+cosx)"d"x=sinx-cosx+C`

Explanation:

We have `I = int(sinx+cosx)"d"x`

By the linearity of the integral, we can rewrite it as:

`I = intsinx"d"x+intcosx"d"x`

These are standard integrals, and are assumed as known:

`int sinx"d"x=-cosx+C_1`
`int cosx"d"x=sinx+C_2`

`=> I = sinx-cosx+C_1+C_2`

Since the sum of two constants is still a constant, denoted `C` in our case, we have the answer we seeked:

`color(Red)(I = sinx-cosx+C)`