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

Integral of e^(-3x) dx

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The solution

You have entered [src] 
  1         
  /         
 |          
 |   -3*x   
 |  E     dx
 |          
/           
0
∫01e−3x dx\int\limits_{0}^{1} e^{- 3 x}\, dx 
Integral(E^(-3*x), (x, 0, 1))
Detail solution

  1. Let u=−3xu = - 3 x.

    Then let du=−3dxdu = - 3 dx and substitute −du3- \frac{du}{3}:

    ∫(−eu3) du\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:

      False\text{False}

      1. The integral of the exponential function is itself.

        ∫eu du=eu\int e^{u}\, du = e^{u}

      So, the result is: −eu3- \frac{e^{u}}{3}

    Now substitute uu back in:

    −e−3x3- \frac{e^{- 3 x}}{3}

  2. Add the constant of integration:

    −e−3x3+constant- \frac{e^{- 3 x}}{3}+ \mathrm{constant}

The answer is:

−e−3x3+constant- \frac{e^{- 3 x}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                    
 |                 -3*x
 |  -3*x          e    
 | E     dx = C - -----
 |                  3  
/
∫e−3x dx=C−e−3x3\int e^{- 3 x}\, dx = C - \frac{e^{- 3 x}}{3}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-1
Plot the graph f(x)
The answer [src] 
     -3
1   e  
- - ---
3    3
13−13e3\frac{1}{3} - \frac{1}{3 e^{3}} 
=
= 
     -3
1   e  
- - ---
3    3
13−13e3\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^(-3x) dx

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

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