Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x*e^(4*x)
Integral of √(1-cos(x))
Integral of x/sqrt(x^2-4x+1)
Integral of xsin^4(x^2)cos^4(x^2)
Identical expressions
(exp^(one /x))/(x^ two)
( exponent of to the power of (1 divide by x)) divide by (x squared )
( exponent of to the power of (one divide by x)) divide by (x to the power of two)
(exp(1/x))/(x2)
exp1/x/x2
(exp^(1/x))/(x²)
(exp to the power of (1/x))/(x to the power of 2)
exp^1/x/x^2
(exp^(1 divide by x)) divide by (x^2)
(exp^(1/x))/(x^2)dx

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

The solution

You have entered [src]

  0         
  /         
 |          
 |  x ___   
 |  \/ E    
 |  ----- dx
 |     2    
 |    x     
 |          
/           
-1

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

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

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = e^{\frac{1}{x}}$ .
  
  Then let $du = - \frac{e^{\frac{1}{x}} dx}{x^{2}}$ and substitute $- du$ :
  
  $\int \left(-1\right)\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\text{False}$
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int 1\, du = u$
    So, the result is: $- u$
  Now substitute $u$ back in:
  
  $- e^{\frac{1}{x}}$
Method #2
1. Let $u = \frac{1}{x}$ .
  
  Then let $du = - \frac{dx}{x^{2}}$ and substitute $- du$ :
  
  $\int \left(- e^{u}\right)\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\text{False}$
    1. The integral of the exponential function is itself.
      
      $\int e^{u}\, du = e^{u}$
    So, the result is: $- e^{u}$
  Now substitute $u$ back in:
  
  $- e^{\frac{1}{x}}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                 
 |                 1
 | x ___           -
 | \/ E            x
 | ----- dx = C - e 
 |    2             
 |   x              
 |                  
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

 -1
e

$$e^{-1}$$

 -1
e

$$e^{-1}$$

exp(-1)

Numerical answer [src]

0.367879441171442

0.367879441171442

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

Other calculators

How to use it?

Identical expressions

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

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2