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Integral of d{x}:
Integral of 4x
Integral of e^(2*x)
Integral of 1/(x^3)
Integral of 1/y
Derivative of:
e^(2*x)
Equation:
e^(2*x)
Limit of the function:
e^(2*x)
Identical expressions
e^(two *x)
e to the power of (2 multiply by x)
e to the power of (two multiply by x)
e(2*x)
e2*x
e^(2x)
e(2x)
e2x
e^2x
e^(2*x)dx
Similar expressions
2e^(2x)
e^(2x)+1
x*e^(2x)
sqrt(2-2e^(2x))

Solving integrals/ e^(2*x)

Integral of e^(2*x) dx

The solution

You have entered [src]

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

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

Detail solution

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:

$\frac{e^{2 x}}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

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

=

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

-1/2 + exp(2)/2

Numerical answer [src]

3.19452804946533

3.19452804946533

The graph

Integral of e^(2*x) dx

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