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Solving integrals/ sinx/(sqrt(cosx+3))

Integral of sinx/(sqrt(cosx+3)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                  
  /                  
 |                   
 |      sin(x)       
 |  -------------- dx
 |    ____________   
 |  \/ cos(x) + 3    
 |                   
/                    
0
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\sqrt{\cos{\left(x \right)} + 3}}\, dx$$ 
Integral(sin(x)/sqrt(cos(x) + 3), (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. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                        
 |                                         
 |     sin(x)                  ____________
 | -------------- dx = C - 2*\/ cos(x) + 3 
 |   ____________                          
 | \/ cos(x) + 3                           
 |                                         
/
$$\int \frac{\sin{\left(x \right)}}{\sqrt{\cos{\left(x \right)} + 3}}\, dx = C - 2 \sqrt{\cos{\left(x \right)} + 3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
        ____________
4 - 2*\/ 3 + cos(1)
$$4 - 2 \sqrt{\cos{\left(1 \right)} + 3}$$ 
=
= 
        ____________
4 - 2*\/ 3 + cos(1)
$$4 - 2 \sqrt{\cos{\left(1 \right)} + 3}$$ 
4 - 2*sqrt(3 + cos(1))
Numerical answer [src] 
0.236861785228643
0.236861785228643

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

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