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Solving integrals/ exp(1/x)

Integral of exp(1/x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1      
  /      
 |       
 |   1   
 |   -   
 |   x   
 |  e  dx
 |       
/        
0
$$\int\limits_{0}^{1} e^{\frac{1}{x}}\, dx$$ 
Integral(exp(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=-2, context=exp(_u)/_u**2, symbol=_u)

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                            
 |                             
 |  1                          
 |  -                          
 |  x                  /   -1 \
 | e  dx = C + x*expint|2, ---|
 |                     \    x /
/
$$\int e^{\frac{1}{x}}\, dx = C + x \operatorname{E}_{2}\left(- \frac{1}{x}\right)$$
Simplify
The answer [src] 
oo - Ei(1)
$$- \operatorname{Ei}{\left(1 \right)} + \infty$$ 
=
= 
oo - Ei(1)
$$- \operatorname{Ei}{\left(1 \right)} + \infty$$ 
oo - Ei(1)
Numerical answer [src] 
3.9130106923273e+4333645441173067313
3.9130106923273e+4333645441173067313

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

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