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Solving integrals/ (sin2x)/(3sin2x-4cos2x)

Integral of (sin2x)/(3sin2x-4cos2x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                           
  /                           
 |                            
 |          sin(2*x)          
 |  ----------------------- dx
 |  3*sin(2*x) - 4*cos(2*x)   
 |                            
/                             
0
$$\int\limits_{0}^{1} \frac{\sin{\left(2 x \right)}}{3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}}\, dx$$ 
Integral(sin(2*x)/(3*sin(2*x) - 4*cos(2*x)), (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

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

    1. Don't know the steps in finding this integral.

      But the integral is

    So, the result is:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                      
 |                                                                       
 |         sin(2*x)                 2*log(-3*sin(2*x) + 4*cos(2*x))   3*x
 | ----------------------- dx = C + ------------------------------- + ---
 | 3*sin(2*x) - 4*cos(2*x)                         25                  25
 |                                                                       
/
$$\int \frac{\sin{\left(2 x \right)}}{3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}}\, dx = C + \frac{3 x}{25} + \frac{2 \log{\left(- 3 \sin{\left(2 x \right)} + 4 \cos{\left(2 x \right)} \right)}}{25}$$
Simplify
The graph
Plot the graph f(x)
Numerical answer [src] 
-2.24697380233999
-2.24697380233999

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

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