Integral of sinx/1+cosx dx

The solution

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

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

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

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\sin{\left(x \right)}}{1}\, dx = \int \sin{\left(x \right)}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- \cos{\left(x \right)}$
  So, the result is: $- \cos{\left(x \right)}$
1. The integral of cosine is sine:
  
  $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
The result is: $\sin{\left(x \right)} - \cos{\left(x \right)}$
Now simplify:

$- \sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}$
Add the constant of integration:

$- \sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}+ \mathrm{constant}$

The answer is:

$- \sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                          
 |                                           
 | /sin(x)         \                         
 | |------ + cos(x)| dx = C - cos(x) + sin(x)
 | \  1            /                         
 |                                           
/

$$\int \left(\frac{\sin{\left(x \right)}}{1} + \cos{\left(x \right)}\right)\, dx = C + \sin{\left(x \right)} - \cos{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$2$$

Numerical answer [src]

2.0

2.0

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

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Integral of sinx/1+cosx dx

Limits of integration:

The graph:

Piecewise:

The solution