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

Asked on by enotes

Textbook Question

Chapter 4, 4.1 - Problem 25 - Calculus of a Single Variable (10th Edition, Ron Larson).
See all solutions for this textbook.

1 Answer | Add Yours

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.`

We’ve answered 319,663 questions. We can answer yours, too.

Ask a question