Integral of (5x-6x²)dx dx

The solution

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  1                
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 |  /         2\   
 |  \5*x - 6*x / dx
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3

$$\int\limits_{3}^{1} \left(- 6 x^{2} + 5 x\right)\, dx$$

Integral(5*x - 6*x^2, (x, 3, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 6 x^{2}\right)\, dx = - 6 \int x^{2}\, dx$
  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: $- 2 x^{3}$
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: $- 2 x^{3} + \frac{5 x^{2}}{2}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                                 
 |                                 2
 | /         2\             3   5*x 
 | \5*x - 6*x / dx = C - 2*x  + ----
 |                               2  
/

$$\int \left(- 6 x^{2} + 5 x\right)\, dx = C - 2 x^{3} + \frac{5 x^{2}}{2}$$

Simplify

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The answer [src]

$$32$$

Numerical answer [src]

32.0

32.0

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

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Integral of (5x-6x²)dx dx

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