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Solving integrals/ exp(x)*sqrt(x)

Integral of exp(x)*sqrt(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

    UpperGammaRule(a=1, e=1/2, context=sqrt(x)*exp(x), symbol=x)

  1. Now simplify:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
                           /              ____     /  ____\\
  /                    ___ |  ____  x   \/ pi *erfc\\/ -x /|
 |                   \/ x *|\/ -x *e  + -------------------|
 |  x   ___                \                     2         /
 | e *\/ x  dx = C + ---------------------------------------
 |                                      ____                
/                                     \/ -x
$$\int \sqrt{x} e^{x}\, dx = C + \frac{\sqrt{x} \left(\sqrt{- x} e^{x} + \frac{\sqrt{\pi} \operatorname{erfc}{\left(\sqrt{- x} \right)}}{2}\right)}{\sqrt{- x}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
        ____       
    I*\/ pi *erf(I)
E + ---------------
           2
$$\frac{i \sqrt{\pi} \operatorname{erf}{\left(i \right)}}{2} + e$$ 
=
= 
        ____       
    I*\/ pi *erf(I)
E + ---------------
           2
$$\frac{i \sqrt{\pi} \operatorname{erf}{\left(i \right)}}{2} + e$$ 
E + i*sqrt(pi)*erf(i)/2
Numerical answer [src] 
1.25563008255186
1.25563008255186

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

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