Integral of cos(x+2) dx

You have entered [src]

  1              
  /              
 |               
 |  cos(x + 2) dx
 |               
/                
0

$$\int\limits_{0}^{1} \cos{\left(x + 2 \right)}\, dx$$

Integral(cos(x + 2), (x, 0, 1))

Detail solution

Let $u = x + 2$ .

Then let $du = dx$ and substitute $du$ :

$\int \cos{\left(u \right)}\, du$
1. The integral of cosine is sine:
  
  $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
Now substitute $u$ back in:

$\sin{\left(x + 2 \right)}$
Now simplify:

$\sin{\left(x + 2 \right)}$
Add the constant of integration:

$\sin{\left(x + 2 \right)}+ \mathrm{constant}$

The answer is:

$\sin{\left(x + 2 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                               
 | cos(x + 2) dx = C + sin(x + 2)
 |                               
/

$$\int \cos{\left(x + 2 \right)}\, dx = C + \sin{\left(x + 2 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-sin(2) + sin(3)

$$- \sin{\left(2 \right)} + \sin{\left(3 \right)}$$

-sin(2) + sin(3)

$$- \sin{\left(2 \right)} + \sin{\left(3 \right)}$$

-sin(2) + sin(3)

Numerical answer [src]

-0.768177418765814

-0.768177418765814

The graph

Use the examples entering the upper and lower limits of integration.