Mister Exam

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How to use it?
Integral of d{x}:
Integral of x*exp(x)
Integral of x*exp(-x)
Integral of xe^(-x/2)
Integral of sqrt(1+(cosx)^2)sinx
Graphing y =:
x*exp(x)
Derivative of:
x*exp(x)
Limit of the function:
x*exp(x)
Identical expressions
x*exp(x)
x multiply by exponent of (x)
xexp(x)
xexpx
x*exp(x)dx
Similar expressions
xexp(x)
xexp^x
xexp(x^4)
x*exp(x^2/2)
x*exp^x^2

Solving integrals/ x*exp(x)

Integral of x*exp(x) dx

The solution

You have entered [src]

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

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 the exponential function is itself.

$\int e^{x}\, dx = e^{x}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$1$$

=

$$1$$

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.