Determine `int cos(3x+4) dx` using substitution.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The integral `int cos(3x+4) dx` has to be determined.

It is known that the integral of cos x is sin x. In cos (3x+4) the cosine of a function of x is being considered.

Use substitution here; let y = 3x + 4

`dy = 3 dx`

`int cos(3x+4) dx`

= `int cos y * (1/3)* dy`

= `(1/3)*int cos y dy`

= `(1/3)*sin y`

replace y by 3x + 4

= `(1/3)*sin(3x+4)`

The integral `int cos(3x+4) dx` is `(sin(3x+4))/3 + C`

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial Team