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Similar expressions
1/(e^(3x)+cos2x)

Integral of 1/(e^(3x)-cos2x) dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |   3*x              
 |  E    - cos(2*x)   
 |                    
/                     
0

$$\int\limits_{0}^{1} \frac{1}{e^{3 x} - \cos{\left(2 x \right)}}\, dx$$

Integral(1/(E^(3*x) - cos(2*x)), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{1}{e^{3 x} - \cos{\left(2 x \right)}} = - \frac{1}{- e^{3 x} + \cos{\left(2 x \right)}}$
The integral of a constant times a function is the constant times the integral of the function:

$\int \left(- \frac{1}{- e^{3 x} + \cos{\left(2 x \right)}}\right)\, dx = - \int \frac{1}{- e^{3 x} + \cos{\left(2 x \right)}}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\int \frac{1}{- e^{3 x} + \cos{\left(2 x \right)}}\, dx$
So, the result is: $- \int \frac{1}{- e^{3 x} + \cos{\left(2 x \right)}}\, dx$
Now simplify:

$- \int \left(- \frac{1}{e^{3 x} - \cos{\left(2 x \right)}}\right)\, dx$
Add the constant of integration:

$- \int \left(- \frac{1}{e^{3 x} - \cos{\left(2 x \right)}}\right)\, dx+ \mathrm{constant}$

The answer is:

$- \int \left(- \frac{1}{e^{3 x} - \cos{\left(2 x \right)}}\right)\, dx+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                           /                    
 |                           |                     
 |        1                  |         1           
 | --------------- dx = C -  | ----------------- dx
 |  3*x                      |    3*x              
 | E    - cos(2*x)           | - e    + cos(2*x)   
 |                           |                     
/                           /

$$\int \frac{1}{e^{3 x} - \cos{\left(2 x \right)}}\, dx = C - \int \frac{1}{- e^{3 x} + \cos{\left(2 x \right)}}\, dx$$

Simplify

The answer [src]

   1                     
   /                     
  |                      
  |          1           
- |  ----------------- dx
  |     3*x              
  |  - e    + cos(2*x)   
  |                      
 /                       
 0

$$- \int\limits_{0}^{1} \frac{1}{- e^{3 x} + \cos{\left(2 x \right)}}\, dx$$

   1                     
   /                     
  |                      
  |          1           
- |  ----------------- dx
  |     3*x              
  |  - e    + cos(2*x)   
  |                      
 /                       
 0

$$- \int\limits_{0}^{1} \frac{1}{- e^{3 x} + \cos{\left(2 x \right)}}\, dx$$

-Integral(1/(-exp(3*x) + cos(2*x)), (x, 0, 1))

Numerical answer [src]

14.2560027374418

14.2560027374418

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

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Integral of 1/(e^(3x)-cos2x) dx

Limits of integration:

The graph:

Piecewise:

The solution