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Similar expressions
(cosx)/(3sinx+1)

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

The solution

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  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

Let $u = 3 \sin{\left(x \right)} - 1$ .

Then let $du = 3 \cos{\left(x \right)} dx$ and substitute $\frac{du}{3}$ :

$\int \frac{1}{3 u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{3}$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  So, the result is: $\frac{\log{\left(u \right)}}{3}$
Now substitute $u$ back in:

$\frac{\log{\left(3 \sin{\left(x \right)} - 1 \right)}}{3}$
Now simplify:

$\frac{\log{\left(3 \sin{\left(x \right)} - 1 \right)}}{3}$
Add the constant of integration:

$\frac{\log{\left(3 \sin{\left(x \right)} - 1 \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{\log{\left(3 \sin{\left(x \right)} - 1 \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
 |                                        
 |    cos(x)             log(3*sin(x) - 1)
 | ------------ dx = C + -----------------
 | 3*sin(x) - 1                  3        
 |                                        
/

$$\int \frac{\cos{\left(x \right)}}{3 \sin{\left(x \right)} - 1}\, dx = C + \frac{\log{\left(3 \sin{\left(x \right)} - 1 \right)}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution