Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x²+4
Integral of x/(raiz(2x-5))
Integral of x^3e^x
Integral of (x+1)/(x^2+2x-1)
Identical expressions
e^dx/sqrt(e^2x- one)
e to the power of dx divide by square root of (e squared x minus 1)
e to the power of dx divide by square root of (e squared x minus one)
e^dx/√(e^2x-1)
edx/sqrt(e2x-1)
edx/sqrte2x-1
e^dx/sqrt(e²x-1)
e to the power of dx/sqrt(e to the power of 2x-1)
e^dx/sqrte^2x-1
e^dx divide by sqrt(e^2x-1)
Similar expressions
e^dx/sqrt(e^2x+1)

Integral of e^dx/sqrt(e^2x-1) dx

The solution

You have entered [src]

 log(3)                
    /                  
   |                   
   |          1        
   |         E         
   |   ------------- dx
   |      __________   
   |     /  2          
   |   \/  E *x - 1    
   |                   
  /                    
log(2)

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

Integral(E^1/sqrt(E^2*x - 1), (x, log(2), log(3)))

Detail solution

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

$\int \frac{e^{1}}{\sqrt{e^{2} x - 1}}\, dx = e \int \frac{1}{\sqrt{e^{2} x - 1}}\, dx$
1. Let $u = \sqrt{e^{2} x - 1}$ .
  
  Then let $du = \frac{e^{2} dx}{2 \sqrt{e^{2} x - 1}}$ and substitute $\frac{2 du}{e^{2}}$ :
  
  $\int \frac{2}{e^{2}}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 1\, du = \frac{2 \int 1\, du}{e^{2}}$
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int 1\, du = u$
    So, the result is: $\frac{2 u}{e^{2}}$
  Now substitute $u$ back in:
  
  $\frac{2 \sqrt{e^{2} x - 1}}{e^{2}}$
So, the result is: $\frac{2 \sqrt{e^{2} x - 1}}{e}$
Now simplify:

$\frac{2 \sqrt{x e^{2} - 1}}{e}$
Add the constant of integration:

$\frac{2 \sqrt{x e^{2} - 1}}{e}+ \mathrm{constant}$

The answer is:

$\frac{2 \sqrt{x e^{2} - 1}}{e}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int \frac{e^{1}}{\sqrt{e^{2} x - 1}}\, dx = C + \frac{2 \sqrt{e^{2} x - 1}}{e}$$

Simplify

Numerical answer [src]

0.469197406839984

0.469197406839984

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of e^dx/sqrt(e^2x-1) dx

Limits of integration:

The graph:

Piecewise:

The solution