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Integral of d{x}:
Integral of sinx
Integral of -exp(-3*x)
Integral of sin(x²)
Integral of (-2)/x^3
Identical expressions
-exp(- three *x)
minus exponent of ( minus 3 multiply by x)
minus exponent of ( minus three multiply by x)
-exp(-3x)
-exp-3x
-exp(-3*x)dx
Similar expressions
-exp(3*x)
exp(-3*x)

Solving integrals/ -exp(-3*x)

Integral of -exp(-3*x) dx

The solution

You have entered [src]

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

$$\int\limits_{0}^{1} \left(- e^{- 3 x}\right)\, dx$$

Integral(-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:

$\int \left(- e^{- 3 x}\right)\, dx = - \int e^{- 3 x}\, dx$
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: $\frac{e^{- 3 x}}{3}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$$\int \left(- e^{- 3 x}\right)\, dx = C + \frac{e^{- 3 x}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

       -3
  1   e  
- - + ---
  3    3

$$- \frac{1}{3} + \frac{1}{3 e^{3}}$$

=

       -3
  1   e  
- - + ---
  3    3

$$- \frac{1}{3} + \frac{1}{3 e^{3}}$$

-1/3 + exp(-3)/3

Numerical answer [src]

-0.316737643877379

-0.316737643877379

The graph

Integral of -exp(-3*x) dx

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