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Identical expressions
(sin2x)/(3sin2x-4cos2x)
( sinus of 2x) divide by (3 sinus of 2x minus 4 co sinus of e of 2x)
sin2x/3sin2x-4cos2x
(sin2x) divide by (3sin2x-4cos2x)
(sin2x)/(3sin2x-4cos2x)dx
Similar expressions
(sin2x)/(3sin2x+4cos2x)

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

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

The solution

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  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

Rewrite the integrand:

$\frac{\sin{\left(2 x \right)}}{3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}} = - \frac{\sin{\left(2 x \right)}}{- 3 \sin{\left(2 x \right)} + 4 \cos{\left(2 x \right)}}$
The integral of a constant times a function is the constant times the integral of the function:

$\int \left(- \frac{\sin{\left(2 x \right)}}{- 3 \sin{\left(2 x \right)} + 4 \cos{\left(2 x \right)}}\right)\, dx = - \int \frac{\sin{\left(2 x \right)}}{- 3 \sin{\left(2 x \right)} + 4 \cos{\left(2 x \right)}}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $- \frac{3 x}{25} - \frac{2 \log{\left(- 3 \sin{\left(2 x \right)} + 4 \cos{\left(2 x \right)} \right)}}{25}$
So, the result is: $\frac{3 x}{25} + \frac{2 \log{\left(- 3 \sin{\left(2 x \right)} + 4 \cos{\left(2 x \right)} \right)}}{25}$
Add the constant of integration:

$\frac{3 x}{25} + \frac{2 \log{\left(- 3 \sin{\left(2 x \right)} + 4 \cos{\left(2 x \right)} \right)}}{25}+ \mathrm{constant}$

The answer is:

$\frac{3 x}{25} + \frac{2 \log{\left(- 3 \sin{\left(2 x \right)} + 4 \cos{\left(2 x \right)} \right)}}{25}+ \mathrm{constant}$

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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Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution