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Integral of d{x}:
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Derivative of:
exp(sqrt(x))
Identical expressions
exp(sqrt(x))
exponent of ( square root of (x))
exp(√(x))
expsqrtx
exp(sqrt(x))dx
Similar expressions
x*exp(sqrt(x)^5)-sqrt(x)/sqr(x)

Solving integrals/ exp(sqrt(x))

Integral of exp(sqrt(x)) dx

The solution

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

Integral(exp(sqrt(x)), (x, 0, 1))

Detail solution

Let $u = \sqrt{x}$ .

Then let $du = \frac{dx}{2 \sqrt{x}}$ and substitute $2 du$ :

$\int 2 u e^{u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int u e^{u}\, du = 2 \int u e^{u}\, du$
  1. Use integration by parts:
    
    $\int \operatorname{u} \operatorname{dv} = \operatorname{u}\operatorname{v} - \int \operatorname{v} \operatorname{du}$
    
    Let $u{\left(u \right)} = u$ and let $\operatorname{dv}{\left(u \right)} = e^{u}$ .
    
    Then $\operatorname{du}{\left(u \right)} = 1$ .
    
    To find $v{\left(u \right)}$ :
    1. The integral of the exponential function is itself.
      
      $\int e^{u}\, du = e^{u}$
    Now evaluate the sub-integral.
  2. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  So, the result is: $2 u e^{u} - 2 e^{u}$
Now substitute $u$ back in:

$2 \sqrt{x} e^{\sqrt{x}} - 2 e^{\sqrt{x}}$
Now simplify:

$2 \left(\sqrt{x} - 1\right) e^{\sqrt{x}}$
Add the constant of integration:

$2 \left(\sqrt{x} - 1\right) e^{\sqrt{x}}+ \mathrm{constant}$

The answer is:

$2 \left(\sqrt{x} - 1\right) e^{\sqrt{x}}+ \mathrm{constant}$

The answer (Indefinite) [src]

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$$\int e^{\sqrt{x}}\, dx = C + 2 \sqrt{x} e^{\sqrt{x}} - 2 e^{\sqrt{x}}$$

Simplify

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The answer [src]

$$2$$

Numerical answer [src]

2.0

2.0

The graph

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

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Identical expressions

Similar expressions

Integral of exp(sqrt(x)) dx

Limits of integration:

The graph:

Piecewise:

The solution