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Solving integrals/ (sinx)/(sqrt(1+2cosx))

Integral of (sinx)/(sqrt(1+2cosx)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                    
  /                    
 |                     
 |       sin(x)        
 |  ---------------- dx
 |    ______________   
 |  \/ 1 + 2*cos(x)    
 |                     
/                      
0
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\sqrt{2 \cos{\left(x \right)} + 1}}\, dx$$ 
Integral(sin(x)/sqrt(1 + 2*cos(x)), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of a constant is the constant times the variable of integration:

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                          
 |                                           
 |      sin(x)                 ______________
 | ---------------- dx = C - \/ 1 + 2*cos(x) 
 |   ______________                          
 | \/ 1 + 2*cos(x)                           
 |                                           
/
$$\int \frac{\sin{\left(x \right)}}{\sqrt{2 \cos{\left(x \right)} + 1}}\, dx = C - \sqrt{2 \cos{\left(x \right)} + 1}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___     ______________
\/ 3  - \/ 1 + 2*cos(1)
$$- \sqrt{1 + 2 \cos{\left(1 \right)}} + \sqrt{3}$$ 
=
= 
  ___     ______________
\/ 3  - \/ 1 + 2*cos(1)
$$- \sqrt{1 + 2 \cos{\left(1 \right)}} + \sqrt{3}$$ 
sqrt(3) - sqrt(1 + 2*cos(1))
Numerical answer [src] 
0.28962070120799
0.28962070120799

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

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