Mister Exam

Other calculators

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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |   3*x     
 |  e   *1 dx
 |           
/            
0
∫01e3x1 dx\int\limits_{0}^{1} e^{3 x} 1\, dx 
Integral(E^(3*x)*1, (x, 0, 1))
Detail solution

  1. Let u=e3xu = e^{3 x}.

    Then let du=3e3xdxdu = 3 e^{3 x} dx and substitute du3\frac{du}{3}:

    ∫19 du\int \frac{1}{9}\, du

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

      ∫13 du=∫1 du3\int \frac{1}{3}\, du = \frac{\int 1\, du}{3}

      1. The integral of a constant is the constant times the variable of integration:

        ∫1 du=u\int 1\, du = u

      So, the result is: u3\frac{u}{3}

    Now substitute uu back in:

    e3x3\frac{e^{3 x}}{3}

  2. Add the constant of integration:

    e3x3+constant\frac{e^{3 x}}{3}+ \mathrm{constant}

The answer is:

e3x3+constant\frac{e^{3 x}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                    
 |                  3*x
 |  3*x            e   
 | e   *1 dx = C + ----
 |                  3  
/
∫e3x1 dx=C+e3x3\int e^{3 x} 1\, dx = C + \frac{e^{3 x}}{3}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90040
Plot the graph f(x)
The answer [src] 
       3
  1   e 
- - + --
  3   3
−13+e33- \frac{1}{3} + \frac{e^{3}}{3} 
=
= 
       3
  1   e 
- - + --
  3   3
−13+e33- \frac{1}{3} + \frac{e^{3}}{3}
Упростить
Numerical answer [src] 
6.36184564106256
6.36184564106256
The graph
Integral of e^(3*x)*dx dx

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

    © Mister Exam – Calculator