Integral of (5x+2) dx

You have entered [src]

  2             
  /             
 |              
 |  (5*x + 2) dx
 |              
/               
-3

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

Integral(5*x + 2, (x, -3, 2))

Detail solution

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

$\frac{x \left(5 x + 4\right)}{2}$
Add the constant of integration:

$\frac{x \left(5 x + 4\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(5 x + 4\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            2
 |                          5*x 
 | (5*x + 2) dx = C + 2*x + ----
 |                           2  
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-5/2

$$- \frac{5}{2}$$

-5/2

$$- \frac{5}{2}$$

Упростить

Numerical answer [src]

-2.5

-2.5

The graph

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