`int (5cos(x) + 4sin(x)) dx` Find the indefinite integral.

1 Answer

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to evaluate the indefinite integral, hence, you need to split the integral, such that:

`int (5cos x + 4sin x) dx = int 5cos x*dx + int 4sin x*dx`

`int 5cos x*dx = 5sin x + c`

`int 4sin x*dx = -4cos x + c`

Gathering the results yields:

`int (5cos x + 4sin x) dx = 5sin x - 4cos x + c`

Hence, evaluating the indefinite integral, yields `int (5cos x + 4sin x) dx = 5sin x - 4cos x + c.`