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Identical expressions
exp(x)*((x- one)/x^ two)
exponent of (x) multiply by ((x minus 1) divide by x squared )
exponent of (x) multiply by ((x minus one) divide by x to the power of two)
exp(x)*((x-1)/x2)
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exp(x)*((x-1)/x²)
exp(x)*((x-1)/x to the power of 2)
exp(x)((x-1)/x^2)
exp(x)((x-1)/x2)
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exp(x)*((x-1) divide by x^2)
exp(x)*((x-1)/x^2)dx
Similar expressions
exp(x)*((x+1)/x^2)

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

The solution

You have entered [src]

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

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

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

Detail solution

There are multiple ways to do this integral.
Method #1
1. Rewrite the integrand:
  
  $\frac{x - 1}{x^{2}} e^{x} = \frac{x e^{x} - e^{x}}{x^{2}}$
2. Rewrite the integrand:
  
  $\frac{x e^{x} - e^{x}}{x^{2}} = \frac{e^{x}}{x} - \frac{e^{x}}{x^{2}}$
3. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{e^{x}}{x^{2}}\right)\, dx = - \int \frac{e^{x}}{x^{2}}\, dx$
    So, the result is: $\frac{\operatorname{E}_{2}\left(- x\right)}{x}$
  The result is: $\operatorname{Ei}{\left(x \right)} + \frac{\operatorname{E}_{2}\left(- x\right)}{x}$
Method #2
1. Rewrite the integrand:
  
  $\frac{x - 1}{x^{2}} e^{x} = \frac{e^{x}}{x} - \frac{e^{x}}{x^{2}}$
2. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{e^{x}}{x^{2}}\right)\, dx = - \int \frac{e^{x}}{x^{2}}\, dx$
    So, the result is: $\frac{\operatorname{E}_{2}\left(- x\right)}{x}$
  The result is: $\operatorname{Ei}{\left(x \right)} + \frac{\operatorname{E}_{2}\left(- x\right)}{x}$
Add the constant of integration:

$\operatorname{Ei}{\left(x \right)} + \frac{\operatorname{E}_{2}\left(- x\right)}{x}+ \mathrm{constant}$

The answer is:

$\operatorname{Ei}{\left(x \right)} + \frac{\operatorname{E}_{2}\left(- x\right)}{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
 |                                        
 |  x x - 1          expint(2, -x)        
 | e *----- dx = C + ------------- + Ei(x)
 |       2                 x              
 |      x                                 
 |                                        
/

$$\int \frac{x - 1}{x^{2}} e^{x}\, dx = C + \operatorname{Ei}{\left(x \right)} + \frac{\operatorname{E}_{2}\left(- x\right)}{x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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$$-\infty$$

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$$-\infty$$

-oo

Numerical answer [src]

-1.3793236779486e+19

-1.3793236779486e+19

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2