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Integral of d{x}:
Integral of e^(2*x)/2
Integral of (2x+1)^(1/2)
Integral of 1/(x(x^2+1))
Integral of x/sqrt(x+2)
Identical expressions
e^(two *x)/ two
e to the power of (2 multiply by x) divide by 2
e to the power of (two multiply by x) divide by two
e(2*x)/2
e2*x/2
e^(2x)/2
e(2x)/2
e2x/2
e^2x/2
e^(2*x) divide by 2
e^(2*x)/2dx

Solving integrals/ e^(2*x)/2

Integral of e^(2*x)/2 dx

The solution

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$$\int\limits_{0}^{1} \frac{e^{2 x}}{2}\, dx$$

Integral(E^(2*x)/2, (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{e^{2 x}}{2}\, dx = \frac{\int e^{2 x}\, dx}{2}$
1. Let $u = 2 x$ .
  
  Then let $du = 2 dx$ and substitute $\frac{du}{2}$ :
  
  $\int \frac{e^{u}}{2}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\text{False}$
    1. The integral of the exponential function is itself.
      
      $\int e^{u}\, du = e^{u}$
    So, the result is: $\frac{e^{u}}{2}$
  Now substitute $u$ back in:
  
  $\frac{e^{2 x}}{2}$
So, the result is: $\frac{e^{2 x}}{4}$
Add the constant of integration:

$\frac{e^{2 x}}{4}+ \mathrm{constant}$

The answer is:

$\frac{e^{2 x}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                  
 |                   
 |  2*x           2*x
 | E             e   
 | ---- dx = C + ----
 |  2             4  
 |                   
/

$$\int \frac{e^{2 x}}{2}\, dx = C + \frac{e^{2 x}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$- \frac{1}{4} + \frac{e^{2}}{4}$$

$$- \frac{1}{4} + \frac{e^{2}}{4}$$

-1/4 + exp(2)/4

Numerical answer [src]

1.59726402473266

1.59726402473266

The graph

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

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Identical expressions

Integral of e^(2*x)/2 dx

Limits of integration:

The graph:

Piecewise:

The solution