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e^(-x)/sqrt(x)
Solving integrals/ e^(-x)/sqrt(x)

Integral of e^(-x)/sqrt(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

        ErfRule(a=-1, b=0, c=0, context=exp(-_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] 
  /                                
 |                                 
 |   -x                            
 |  E               ____    /  ___\
 | ----- dx = C + \/ pi *erf\\/ x /
 |   ___                           
 | \/ x                            
 |                                 
/
$$\int \frac{e^{- x}}{\sqrt{x}}\, dx = C + \sqrt{\pi} \operatorname{erf}{\left(\sqrt{x} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ____       
\/ pi *erf(1)
$$\sqrt{\pi} \operatorname{erf}{\left(1 \right)}$$ 
=
= 
  ____       
\/ pi *erf(1)
$$\sqrt{\pi} \operatorname{erf}{\left(1 \right)}$$ 
sqrt(pi)*erf(1)
Numerical answer [src] 
1.49364826509427
1.49364826509427
The graph
Integral of e^(-x)/sqrt(x) dx

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

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