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Graphing y =:
x+3x^2
Identical expressions
x+3x^ two
x plus 3x squared
x plus 3x to the power of two
x+3x2
x+3x²
x+3x to the power of 2
x+3x^2dx
Similar expressions
x-3x^2

Solving integrals/ x+3x^2

Integral of x+3x^2 dx

The solution

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  1              
  /              
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 |  /       2\   
 |  \x + 3*x / dx
 |               
/                
0

$$\int\limits_{0}^{1} \left(3 x^{2} + x\right)\, dx$$

Integral(x + 3*x^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 3 x^{2}\, dx = 3 \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $x^{3}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
The result is: $x^{3} + \frac{x^{2}}{2}$
Now simplify:

$x^{2} \left(x + \frac{1}{2}\right)$
Add the constant of integration:

$x^{2} \left(x + \frac{1}{2}\right)+ \mathrm{constant}$

The answer is:

$x^{2} \left(x + \frac{1}{2}\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int \left(3 x^{2} + x\right)\, dx = C + x^{3} + \frac{x^{2}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

3/2

$$\frac{3}{2}$$

3/2

$$\frac{3}{2}$$

3/2

Numerical answer [src]

1.5

1.5

The graph

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

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Identical expressions

Similar expressions

Integral of x+3x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution