# Integral of cos x

How to solve the given integral by using the integral of cos x: formula, 1 example, and its solution.

## Formula

Recall that

the derivative of sin x is cos x.

And integral and derivative

are the opposite operations.

So the integral of cos x is

sin x + C.

For an indefinite integral,

there should be +C.

## Example∫ cos^{2} x/2 dx

Solution

Solution (Detail)

cos^{2} x/2 = [1 + cos x]/2

cos A/2

Take the denomiator 1/2 out from the integral.

Solve the integral.

First write the coefficient 1/2.

The integral of 1 is x.

Integral of a Polynomial

The integral of cos x is sin x.

The given integral is an indefinite integral.

So write +C.

So

(1/2)(x + sin x) + C

is the answer.