Mister Exam

Other calculators


sinx/(1+3cosx)

Integral of sinx/(1+3cosx) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  0                
  /                
 |                 
 |     sin(x)      
 |  ------------ dx
 |  1 + 3*cos(x)   
 |                 
/                  
0                  
$$\int\limits_{0}^{0} \frac{\sin{\left(x \right)}}{3 \cos{\left(x \right)} + 1}\, dx$$
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 is .

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                       
 |                                        
 |    sin(x)             log(1 + 3*cos(x))
 | ------------ dx = C - -----------------
 | 1 + 3*cos(x)                  3        
 |                                        
/                                         
$$-{{\log \left(3\,\cos x+1\right)}\over{3}}$$
The graph
The answer [src]
0
$$0$$
=
=
0
$$0$$
Numerical answer [src]
0.0
0.0
The graph
Integral of sinx/(1+3cosx) dx

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