Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of e^(2*x)/x
Integral of e^(x*(-5))
Integral of cos(x)^6
Integral of 1/(x*(lnx)^2)
Derivative of:
e^x*sqrt(x)
Limit of the function:
e^x*sqrt(x)
Identical expressions
e^x*sqrt(x)
e to the power of x multiply by square root of (x)
e^x*√(x)
ex*sqrt(x)
ex*sqrtx
e^xsqrt(x)
exsqrt(x)
exsqrtx
e^xsqrtx
e^x*sqrt(x)dx

Integral of e^x*sqrt(x) dx

The solution

You have entered [src]

  1            
  /            
 |             
 |   x   ___   
 |  E *\/ x  dx
 |             
/              
0

$$\int\limits_{0}^{1} e^{x} \sqrt{x}\, dx$$

Integral(E^x*sqrt(x), (x, 0, 1))

Detail solution

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

Now simplify:

$\sqrt{x} e^{x} + \frac{\sqrt{\pi} \sqrt{x} \operatorname{erfc}{\left(\sqrt{- x} \right)}}{2 \sqrt{- x}}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

                           /              ____     /  ____\\
  /                    ___ |  ____  x   \/ pi *erfc\\/ -x /|
 |                   \/ x *|\/ -x *e  + -------------------|
 |  x   ___                \                     2         /
 | E *\/ x  dx = C + ---------------------------------------
 |                                      ____                
/                                     \/ -x

$$\int e^{x} \sqrt{x}\, dx = C + \frac{\sqrt{x} \left(\sqrt{- x} e^{x} + \frac{\sqrt{\pi} \operatorname{erfc}{\left(\sqrt{- x} \right)}}{2}\right)}{\sqrt{- x}}$$

Simplify

The graph

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.

Other calculators

How to use it?

Identical expressions

Integral of e^x*sqrt(x) dx

Limits of integration:

The graph:

Piecewise:

The solution