Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^2*e^(x*(-2))
Integral of e^(-x^3)
Integral of -exp(-3*x)
Integral of (1-2*x)/x^2
Identical expressions
(one / three)*exp(3x) two
(1 divide by 3) multiply by exponent of (3x)2
(one divide by three) multiply by exponent of (3x) two
(1/3)exp(3x)2
1/3exp3x2
(1 divide by 3)*exp(3x)2
(1/3)*exp(3x)2dx

Integral of (1/3)*exp(3x)2 dx

The solution

You have entered [src]

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

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

Integral((exp(3*x)/3)*2, (x, 0, 1))

Detail solution

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

$\int 2 \frac{e^{3 x}}{3}\, dx = 2 \int \frac{e^{3 x}}{3}\, dx$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{e^{3 x}}{3}\, dx = \frac{\int e^{3 x}\, dx}{3}$
  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: $\frac{e^{3 x}}{9}$
So, the result is: $\frac{2 e^{3 x}}{9}$
Add the constant of integration:

$\frac{2 e^{3 x}}{9}+ \mathrm{constant}$

The answer is:

$\frac{2 e^{3 x}}{9}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                       
 |  3*x               3*x
 | e               2*e   
 | ----*2 dx = C + ------
 |  3                9   
 |                       
/

$$\int 2 \frac{e^{3 x}}{3}\, dx = C + \frac{2 e^{3 x}}{9}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

         3
  2   2*e 
- - + ----
  9    9

$$- \frac{2}{9} + \frac{2 e^{3}}{9}$$

         3
  2   2*e 
- - + ----
  9    9

$$- \frac{2}{9} + \frac{2 e^{3}}{9}$$

-2/9 + 2*exp(3)/9

Numerical answer [src]

4.24123042737504

4.24123042737504

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

Other calculators

How to use it?

Identical expressions

Integral of (1/3)*exp(3x)2 dx

Limits of integration:

The graph:

Piecewise:

The solution