Mister Exam

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How to use it?
Integral of d{x}:
Integral of 1/5x
Integral of x*dx/(x^2+1)
Integral of x^3*exp(x^2)
Integral of x^2*a^x
Graphing y =:
-x*exp(x)
Limit of the function:
-x*exp(x)
Identical expressions
-x*exp(x)
minus x multiply by exponent of (x)
-xexp(x)
-xexpx
-x*exp(x)dx
Similar expressions
(3-x)*exp(x)
-xexp(x)
x*exp(x)
sin(2(3-x))exp(x)
(1-x)*exp(x)*y^(2)-x*y

Solving integrals/ -x*exp(x)

Integral of -x*exp(x) dx

The solution

You have entered [src]

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

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

Integral((-x)*exp(x), (x, 0, 1))

Detail solution

Use integration by parts:

$\int \operatorname{u} \operatorname{dv} = \operatorname{u}\operatorname{v} - \int \operatorname{v} \operatorname{du}$

Let $u{\left(x \right)} = - x$ and let $\operatorname{dv}{\left(x \right)} = e^{x}$ .

Then $\operatorname{du}{\left(x \right)} = -1$ .

To find $v{\left(x \right)}$ :
1. The integral of the exponential function is itself.
  
  $\int e^{x}\, dx = e^{x}$
Now evaluate the sub-integral.
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. The integral of the exponential function is itself.
  
  $\int e^{x}\, dx = e^{x}$
So, the result is: $- e^{x}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                        
 |                         
 |     x             x    x
 | -x*e  dx = C - x*e  + e 
 |                         
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1

$$-1$$

=

-1

$$-1$$

-1

Numerical answer [src]

-1.0

-1.0

The graph

Integral of -x*exp(x) dx

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