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Identical expressions
exp^(one /x)/x^ three
exponent of to the power of (1 divide by x) divide by x cubed
exponent of to the power of (one divide by x) divide by x to the power of three
exp(1/x)/x3
exp1/x/x3
exp^(1/x)/x³
exp to the power of (1/x)/x to the power of 3
exp^1/x/x^3
exp^(1 divide by x) divide by x^3
exp^(1/x)/x^3dx

Solving integrals/ exp^(1/x)/x^3

Integral of exp^(1/x)/x^3 dx

The solution

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  1         
  /         
 |          
 |  x ___   
 |  \/ E    
 |  ----- dx
 |     3    
 |    x     
 |          
/           
0

$$\int\limits_{0}^{1} \frac{e^{\frac{1}{x}}}{x^{3}}\, dx$$

Integral(E^(1/x)/x^3, (x, 0, 1))

Detail solution

Let $u = \frac{1}{x}$ .

Then let $du = - \frac{dx}{x^{2}}$ and substitute $- du$ :

$\int \left(- u e^{u}\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int u e^{u}\, du = - \int u e^{u}\, du$
  1. Use integration by parts:
    
    $\int \operatorname{u} \operatorname{dv} = \operatorname{u}\operatorname{v} - \int \operatorname{v} \operatorname{du}$
    
    Let $u{\left(u \right)} = u$ and let $\operatorname{dv}{\left(u \right)} = e^{u}$ .
    
    Then $\operatorname{du}{\left(u \right)} = 1$ .
    
    To find $v{\left(u \right)}$ :
    1. The integral of the exponential function is itself.
      
      $\int e^{u}\, du = e^{u}$
    Now evaluate the sub-integral.
  2. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  So, the result is: $- u e^{u} + e^{u}$
Now substitute $u$ back in:

$e^{\frac{1}{x}} - \frac{e^{\frac{1}{x}}}{x}$
Now simplify:

$\frac{\left(x - 1\right) e^{\frac{1}{x}}}{x}$
Add the constant of integration:

$\frac{\left(x - 1\right) e^{\frac{1}{x}}}{x}+ \mathrm{constant}$

The answer is:

$\frac{\left(x - 1\right) e^{\frac{1}{x}}}{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                1     
 |                 -    1
 | x ___           x    -
 | \/ E           e     x
 | ----- dx = C - -- + e 
 |    3           x      
 |   x                   
 |                       
/

$$\int \frac{e^{\frac{1}{x}}}{x^{3}}\, dx = C + e^{\frac{1}{x}} - \frac{e^{\frac{1}{x}}}{x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

3.88961330679057e+4333645441173067370

3.88961330679057e+4333645441173067370

The graph

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

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Identical expressions

Integral of exp^(1/x)/x^3 dx

Limits of integration:

The graph:

Piecewise:

The solution