Integral of (5*x-1) dx

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 |  (5*x - 1) dx
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1

$$\int\limits_{1}^{2} \left(5 x - 1\right)\, dx$$

Integral(5*x - 1*1, (x, 1, 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:
  
  $\int \left(\left(-1\right) 1\right)\, dx = - x$
The result is: $\frac{5 x^{2}}{2} - x$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                          2
 |                        5*x 
 | (5*x - 1) dx = C - x + ----
 |                         2  
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$${{5\,x^2}\over{2}}-x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

13/2

$${{13}\over{2}}$$

13/2

$$\frac{13}{2}$$

Упростить

Numerical answer [src]

6.5

6.5

The graph

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