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xe^(1/x)
Solving integrals/ xe^(1/x)

Integral of xe^(1/x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |    x ___   
 |  x*\/ E  dx
 |            
/             
0
$$\int\limits_{0}^{1} e^{\frac{1}{x}} x\, dx$$ 
Integral(x*E^(1/x), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

    1. The integral of a constant times a function is the constant times the integral of the function:

        UpperGammaRule(a=1, e=-3, context=exp(_u)/_u**3, symbol=_u)

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                  
 |                                   
 |   x ___           2       /   -1 \
 | x*\/ E  dx = C + x *expint|3, ---|
 |                           \    x /
/
$$\int e^{\frac{1}{x}} x\, dx = C + x^{2} \operatorname{E}_{3}\left(- \frac{1}{x}\right)$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
     Ei(1)
oo - -----
       2
$$- \frac{\operatorname{Ei}{\left(1 \right)}}{2} + \infty$$ 
=
= 
     Ei(1)
oo - -----
       2
$$- \frac{\operatorname{Ei}{\left(1 \right)}}{2} + \infty$$ 
oo - Ei(1)/2
Numerical answer [src] 
3.92310711940104e+4333645441173067294
3.92310711940104e+4333645441173067294
The graph
Integral of xe^(1/x) dx

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

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