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Integral of d{x}:
Integral of x^2/sqrt(1+x^2)
Integral of 1/√(1-4x^2)
Integral of sin^3x/cosx
Integral of 3*exp(-3*x)
Identical expressions
three *exp(- three *x)
3 multiply by exponent of ( minus 3 multiply by x)
three multiply by exponent of ( minus three multiply by x)
3exp(-3x)
3exp-3x
3*exp(-3*x)dx
Similar expressions
3*exp(3*x)
(x^(-2/3))*exp(-3*x^(1/3))

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

Integral of 3exp(-3x) dx

The solution

You have entered [src]

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

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

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

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

     -3
1 - e

$$1 - e^{-3}$$

=

     -3
1 - e

$$1 - e^{-3}$$

1 - exp(-3)

Numerical answer [src]

0.950212931632136

0.950212931632136

The graph

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

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