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Integral of d{x}:
Integral of (x²+1)dx
Integral of sqrt(4-x^2)/x^2
Integral of sin(log(x))/xdx
Integral of sin²(x)+cos²(x)
Graphing y =:
x-e^-x
Derivative of:
x-e^-x
Identical expressions
x-e^-x
x minus e to the power of minus x
x-e-x
x-e^-xdx
Similar expressions
x-e^+x
x+e^-x

Solving integrals/ x-e^-x

Integral of x-e^-x dx

The solution

You have entered [src]

  1             
  /             
 |              
 |  /     -x\   
 |  \x - e  / dx
 |              
/               
0

$$\int\limits_{0}^{1} \left(x - e^{- x}\right)\, dx$$

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

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- e^{- x}\right)\, dx = - \int e^{- x}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- e^{- x}$
  So, the result is: $e^{- x}$
The result is: $\frac{x^{2}}{2} + e^{- x}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                           
 |                     2      
 | /     -x\          x     -x
 | \x - e  / dx = C + -- + e  
 |                    2       
/

$$e^ {- x }+{{x^2}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  1    -1
- - + e  
  2

$$-{{e^ {- 1 }\,\left(e-2\right)}\over{2}}$$

  1    -1
- - + e  
  2

$$- \frac{1}{2} + e^{-1}$$

Simplify

Numerical answer [src]

-0.132120558828558

-0.132120558828558

The graph

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

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Identical expressions

Similar expressions

Integral of x-e^-x dx

Limits of integration:

The graph:

Piecewise:

The solution