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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] 
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∫01exx dx\int\limits_{0}^{1} e^{x} \sqrt{x}\, dx 
Integral(E^x*sqrt(x), (x, 0, 1))
Detail solution

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

  1. Now simplify:

    xex+πxerfc⁡(−x)2−x\sqrt{x} e^{x} + \frac{\sqrt{\pi} \sqrt{x} \operatorname{erfc}{\left(\sqrt{- x} \right)}}{2 \sqrt{- x}}

  2. Add the constant of integration:

    xex+πxerfc⁡(−x)2−x+constant\sqrt{x} e^{x} + \frac{\sqrt{\pi} \sqrt{x} \operatorname{erfc}{\left(\sqrt{- x} \right)}}{2 \sqrt{- x}}+ \mathrm{constant}

The answer is:

xex+πxerfc⁡(−x)2−x+constant\sqrt{x} e^{x} + \frac{\sqrt{\pi} \sqrt{x} \operatorname{erfc}{\left(\sqrt{- x} \right)}}{2 \sqrt{- x}}+ \mathrm{constant}

The answer (Indefinite) [src] 
                           /              ____     /  ____\\
  /                    ___ |  ____  x   \/ pi *erfc\\/ -x /|
 |                   \/ x *|\/ -x *e  + -------------------|
 |  x   ___                \                     2         /
 | E *\/ x  dx = C + ---------------------------------------
 |                                      ____                
/                                     \/ -x
∫exx dx=C+x(−xex+πerfc⁡(−x)2)−x\int e^{x} \sqrt{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
0.001.000.100.200.300.400.500.600.700.800.900.05.0
Plot the graph f(x)
The answer [src] 
        ____       
    I*\/ pi *erf(I)
E + ---------------
           2
iπerf⁡(i)2+e\frac{i \sqrt{\pi} \operatorname{erf}{\left(i \right)}}{2} + e 
=
= 
        ____       
    I*\/ pi *erf(I)
E + ---------------
           2
iπerf⁡(i)2+e\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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