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Integral of (cosx)/(3sinx-1) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

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

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                       
 |                                        
 |    cos(x)             log(3*sin(x) - 1)
 | ------------ dx = C + -----------------
 | 3*sin(x) - 1                  3        
 |                                        
/                                         
$$\int \frac{\cos{\left(x \right)}}{3 \sin{\left(x \right)} - 1}\, dx = C + \frac{\log{\left(3 \sin{\left(x \right)} - 1 \right)}}{3}$$
The graph
The answer [src]
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Numerical answer [src]
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    Use the examples entering the upper and lower limits of integration.