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Identical expressions
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(two divide by sinus of squared x minus 3e to the power of x)
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Similar expressions
(2/sin^2x+3e^x)

Solving integrals/ (2/sin^2x-3e^x)

Integral of (2/sin^2x-3e^x) dx

The solution

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  1                    
  /                    
 |                     
 |  /   2         x\   
 |  |------- - 3*e | dx
 |  |   2          |   
 |  \sin (x)       /   
 |                     
/                      
0

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

Simplify

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 3 e^{x}\right)\, dx = - \int 3 e^{x}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 3 e^{x}\, dx = 3 \int e^{x}\, dx$
    1. The integral of the exponential function is itself.
      
      $\int e^{x}\, dx = e^{x}$
    So, the result is: $3 e^{x}$
  So, the result is: $- 3 e^{x}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{2}{\sin^{2}{\left(x \right)}}\, dx = 2 \int \frac{1}{\sin^{2}{\left(x \right)}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
  So, the result is: $- \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}$
The result is: $- 3 e^{x} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}$
Now simplify:

$- 3 e^{x} - \frac{2}{\tan{\left(x \right)}}$
Add the constant of integration:

$- 3 e^{x} - \frac{2}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer is:

$- 3 e^{x} - \frac{2}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                          
 | /   2         x\             x   2*cos(x)
 | |------- - 3*e | dx = C - 3*e  - --------
 | |   2          |                  sin(x) 
 | \sin (x)       /                         
 |                                          
/

$$-{{2}\over{\tan x}}-3\,e^{x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$${\it \%a}$$

oo

$$\infty$$

Simplify

Numerical answer [src]

2.75864735589719e+19

2.75864735589719e+19

The graph

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

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Identical expressions

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Integral of (2/sin^2x-3e^x) dx

Limits of integration:

The graph:

Piecewise:

The solution