Mister Exam

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Graphing y =:
sin(x)/(cos(x)+2)
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Similar expressions
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Solving integrals/ sin(x)/(cos(x)+2)

Integral of sin(x)/(cos(x)+2) dx

The solution

You have entered [src]

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

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

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

Detail solution

Let $u = \cos{\left(x \right)} + 2$ .

Then let $du = - \sin{\left(x \right)} dx$ and substitute $- du$ :

$\int \left(- \frac{1}{u}\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{u}\, du = - \int \frac{1}{u}\, du$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  So, the result is: $- \log{\left(u \right)}$
Now substitute $u$ back in:

$- \log{\left(\cos{\left(x \right)} + 2 \right)}$
Now simplify:

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

$- \log{\left(\cos{\left(x \right)} + 2 \right)}+ \mathrm{constant}$

The answer is:

$- \log{\left(\cos{\left(x \right)} + 2 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-log(2 + cos(1)) + log(3)

$$- \log{\left(\cos{\left(1 \right)} + 2 \right)} + \log{\left(3 \right)}$$

-log(2 + cos(1)) + log(3)

$$- \log{\left(\cos{\left(1 \right)} + 2 \right)} + \log{\left(3 \right)}$$

-log(2 + cos(1)) + log(3)

Numerical answer [src]

0.166329196661429

0.166329196661429

The graph

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

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Identical expressions

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Integral of sin(x)/(cos(x)+2) dx

Limits of integration:

The graph:

Piecewise:

The solution