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Integral of d{x}:
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Integral of dy/y^2
Identical expressions
two x+3x^2
2x plus 3x squared
two x plus 3x squared
2x+3x2
2x+3x²
2x+3x to the power of 2
2x+3x^2dx
Similar expressions
2x-3x^2

Integral of 2x+3x^2 dx

The solution

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  5                
  /                
 |                 
 |  /         2\   
 |  \2*x + 3*x / dx
 |                 
/                  
0

$$\int\limits_{0}^{5} \left(3 x^{2} + 2 x\right)\, dx$$

Integral(2*x + 3*x^2, (x, 0, 5))

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$150$$

Numerical answer [src]

150.0

150.0

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

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Integral of 2x+3x^2 dx

Limits of integration:

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Piecewise:

The solution