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Integral of d{x}:
Integral of cosx
Integral of y^(-2/3)
Integral of (2x-4)
Integral of 3*exp(-2*x)
Identical expressions
three *exp(- two *x)
3 multiply by exponent of ( minus 2 multiply by x)
three multiply by exponent of ( minus two multiply by x)
3exp(-2x)
3exp-2x
3*exp(-2*x)dx
Similar expressions
x^3*exp(-2*x^2)
3*exp(2*x)
x^(3)exp(-2x)
x^3exp(-2x^2)

Solving integrals/ 3*exp(-2*x)

Integral of 3exp(-2x) dx

The solution

You have entered [src]

  1           
  /           
 |            
 |     -2*x   
 |  3*e     dx
 |            
/             
0

$$\int\limits_{0}^{1} 3 e^{- 2 x}\, dx$$

Integral(3*exp(-2*x), (x, 0, 1))

Detail solution

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

$\int 3 e^{- 2 x}\, dx = 3 \int e^{- 2 x}\, dx$
1. Let $u = - 2 x$ .
  
  Then let $du = - 2 dx$ and substitute $- \frac{du}{2}$ :
  
  $\int \left(- \frac{e^{u}}{2}\right)\, du$
  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: $- \frac{3 e^{- 2 x}}{2}$
Add the constant of integration:

$- \frac{3 e^{- 2 x}}{2}+ \mathrm{constant}$

The answer is:

$- \frac{3 e^{- 2 x}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                        
 |                     -2*x
 |    -2*x          3*e    
 | 3*e     dx = C - -------
 |                     2   
/

$$\int 3 e^{- 2 x}\, dx = C - \frac{3 e^{- 2 x}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

       -2
3   3*e  
- - -----
2     2

$$\frac{3}{2} - \frac{3}{2 e^{2}}$$

=

       -2
3   3*e  
- - -----
2     2

$$\frac{3}{2} - \frac{3}{2 e^{2}}$$

3/2 - 3*exp(-2)/2

Numerical answer [src]

1.29699707514508

1.29699707514508

The graph

Integral of 3*exp(-2*x) dx

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