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

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`