Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of sin(5x)
Integral of 2/sinx
Integral of √(1-cos(x))
Integral of y=5x
Identical expressions
two *exp(three *x)
2 multiply by exponent of (3 multiply by x)
two multiply by exponent of (three multiply by x)
2exp(3x)
2exp3x
2*exp(3*x)dx
Similar expressions
x^2*exp(3x+1)
x^2*exp(3x)
x^2exp^(3)x

Solving integrals/ 2*exp(3*x)

Integral of 2exp(3x) dx

The solution

You have entered [src]

  1          
  /          
 |           
 |     3*x   
 |  2*e    dx
 |           
/            
0

\int\limits_{0}^{1} 2 e^{3 x}\, dx

Integral(2*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:

$\int 2 e^{3 x}\, dx = 2 \int e^{3 x}\, dx$
1. Let $u = 3 x$ .
  
  Then let $du = 3 dx$ and substitute $\frac{du}{3}$ :
  
  $\int \frac{e^{u}}{3}\, du$
  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: $\frac{2 e^{3 x}}{3}$
Add the constant of integration:

$\frac{2 e^{3 x}}{3}+ \mathrm{constant}$

The answer is:

\frac{2 e^{3 x}}{3}+ \mathrm{constant}

The answer (Indefinite) [src]

  /                      
 |                    3*x
 |    3*x          2*e   
 | 2*e    dx = C + ------
 |                   3   
/

\int 2 e^{3 x}\, dx = C + \frac{2 e^{3 x}}{3}

Simplify

The graph

Plot the graph f(x)

The answer [src]

         3
  2   2*e 
- - + ----
  3    3

- \frac{2}{3} + \frac{2 e^{3}}{3}

=

         3
  2   2*e 
- - + ----
  3    3

- \frac{2}{3} + \frac{2 e^{3}}{3}

-2/3 + 2*exp(3)/3

Numerical answer [src]

12.7236912821251

12.7236912821251

The graph

Integral of 2*exp(3*x) dx

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