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Graphing y =:
5x+x^2
Identical expressions
5x+x^ two
5x plus x squared
5x plus x to the power of two
5x+x2
5x+x²
5x+x to the power of 2
5x+x^2dx
Similar expressions
5x-x^2

Integral of 5x+x^2 dx

The solution

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

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

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

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 5 x\, dx = 5 \int x\, dx$
  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: $\frac{5 x^{2}}{2}$
The result is: $\frac{x^{3}}{3} + \frac{5 x^{2}}{2}$
Now simplify:

$\frac{x^{2} \left(2 x + 15\right)}{6}$
Add the constant of integration:

$\frac{x^{2} \left(2 x + 15\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(2 x + 15\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                      3      2
 | /       2\          x    5*x 
 | \5*x + x / dx = C + -- + ----
 |                     3     2  
/

$$\int \left(x^{2} + 5 x\right)\, dx = C + \frac{x^{3}}{3} + \frac{5 x^{2}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

63/2

$$\frac{63}{2}$$

63/2

$$\frac{63}{2}$$

63/2

Numerical answer [src]

31.5

31.5

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

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Integral of 5x+x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution