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Integral of d{x}:
Integral of x*e^(x*(-2))
Integral of e^(x*(-3))*dx
Integral of e^(x+e^x)
Integral of 4x^-2
Identical expressions
e^(x*(- three))*dx
e to the power of (x multiply by ( minus 3)) multiply by dx
e to the power of (x multiply by ( minus three)) multiply by dx
e(x*(-3))*dx
ex*-3*dx
e^(x(-3))dx
e(x(-3))dx
ex-3dx
e^x-3dx
Similar expressions
e^(x*(3))*dx

Solving integrals/ e^(x*(-3))*dx

Integral of e^(x(-3))dx dx

The solution

You have entered [src]

  1           
  /           
 |            
 |   x*(-3)   
 |  E       dx
 |            
/             
0

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

Integral(E^(x*(-3)), (x, 0, 1))

Detail solution

Let $u = \left(-3\right) x$ .

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:

$- \frac{e^{\left(-3\right) x}}{3}$
Now simplify:

$- \frac{e^{- 3 x}}{3}$
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]

  /                        
 |                   x*(-3)
 |  x*(-3)          e      
 | E       dx = C - -------
 |                     3   
/

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

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 e^(x*(-3))*dx dx

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