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Graphing y =:
5x^2-3x-1
Identical expressions
5x^ two -3x- one
5x squared minus 3x minus 1
5x to the power of two minus 3x minus one
5x2-3x-1
5x²-3x-1
5x to the power of 2-3x-1
5x^2-3x-1dx
Similar expressions
5x^2+3x-1
5x^2-3x+1

Integral of 5x^2-3x-1 dx

The solution

You have entered [src]

  1                    
  /                    
 |                     
 |  /   2          \   
 |  \5*x  - 3*x - 1/ dx
 |                     
/                      
-1

$$\int\limits_{-1}^{1} \left(\left(5 x^{2} - 3 x\right) - 1\right)\, dx$$

Integral(5*x^2 - 3*x - 1, (x, -1, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 5 x^{2}\, dx = 5 \int x^{2}\, dx$
    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: $\frac{5 x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 3 x\right)\, dx = - 3 \int x\, dx$
    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: $- \frac{3 x^{2}}{2}$
  The result is: $\frac{5 x^{3}}{3} - \frac{3 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-1\right)\, dx = - x$
The result is: $\frac{5 x^{3}}{3} - \frac{3 x^{2}}{2} - x$
Now simplify:

$\frac{x \left(10 x^{2} - 9 x - 6\right)}{6}$
Add the constant of integration:

$\frac{x \left(10 x^{2} - 9 x - 6\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(10 x^{2} - 9 x - 6\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                  2      3
 | /   2          \              3*x    5*x 
 | \5*x  - 3*x - 1/ dx = C - x - ---- + ----
 |                                2      3  
/

$$\int \left(\left(5 x^{2} - 3 x\right) - 1\right)\, dx = C + \frac{5 x^{3}}{3} - \frac{3 x^{2}}{2} - x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

4/3

$$\frac{4}{3}$$

4/3

$$\frac{4}{3}$$

4/3

Numerical answer [src]

1.33333333333333

1.33333333333333

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

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Integral of 5x^2-3x-1 dx

Limits of integration:

The graph:

Piecewise:

The solution