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Solving integrals/ exp(x)/(1-exp(2x))^1/2

Integral of exp(x)/(1-exp(2x))^1/2 dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |         x        
 |        e         
 |  ------------- dx
 |     __________   
 |    /      2*x    
 |  \/  1 - e       
 |                  
/                   
0

$$\int\limits_{0}^{1} \frac{e^{x}}{\sqrt{1 - e^{2 x}}}\, dx$$

Integral(exp(x)/(sqrt(1 - exp(2*x))), (x, 0, 1))

Detail solution

Let $u = e^{x}$ .

Then let $du = e^{x} dx$ and substitute $du$ :

$\int \frac{1}{\sqrt{1 - u^{2}}}\, du$
Now substitute $u$ back in:

$\operatorname{asin}{\left(e^{x} \right)}$
Add the constant of integration:

$\operatorname{asin}{\left(e^{x} \right)}+ \mathrm{constant}$

The answer is:

$\operatorname{asin}{\left(e^{x} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                                
 |        x                       
 |       e                    / x\
 | ------------- dx = C + asin\e /
 |    __________                  
 |   /      2*x                   
 | \/  1 - e                      
 |                                
/

$$\arcsin e^{x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  pi          
- -- + asin(e)
  2

$$\arcsin e-{{\pi}\over{2}}$$

  pi          
- -- + asin(e)
  2

$$- \frac{\pi}{2} + \operatorname{asin}{\left(e \right)}$$

Упростить

Numerical answer [src]

(0.0 - 1.65745445377797j)

(0.0 - 1.65745445377797j)

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

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Identical expressions

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Integral of exp(x)/(1-exp(2x))^1/2 dx

Limits of integration:

The graph:

Piecewise:

The solution