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Integral of d{x}:
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Integral of 1/(x^2-2*x)
Identical expressions
(- four *y^ two - fifteen)/ fifteen
( minus 4 multiply by y squared minus 15) divide by 15
( minus four multiply by y to the power of two minus fifteen) divide by fifteen
(-4*y2-15)/15
-4*y2-15/15
(-4*y²-15)/15
(-4*y to the power of 2-15)/15
(-4y^2-15)/15
(-4y2-15)/15
-4y2-15/15
-4y^2-15/15
(-4*y^2-15) divide by 15
Similar expressions
(4*y^2-15)/15
(-4*y^2+15)/15

Integral of (-4*y^2-15)/15 dy

The solution

You have entered [src]

   ____               
 \/ 15                
    /                 
   |                  
   |         2        
   |    - 4*y  - 15   
   |    ----------- dy
   |         15       
   |                  
  /                   
   ____               
-\/ 15

$$\int\limits_{- \sqrt{15}}^{\sqrt{15}} \frac{- 4 y^{2} - 15}{15}\, dy$$

Integral((-4*y^2 - 15)/15, (y, -sqrt(15), sqrt(15)))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{- 4 y^{2} - 15}{15}\, dy = \frac{\int \left(- 4 y^{2} - 15\right)\, dy}{15}$
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 4 y^{2}\right)\, dy = - 4 \int y^{2}\, dy$
    1. The integral of $y^{n}$ is $\frac{y^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int y^{2}\, dy = \frac{y^{3}}{3}$
    So, the result is: $- \frac{4 y^{3}}{3}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int \left(-15\right)\, dy = - 15 y$
  The result is: $- \frac{4 y^{3}}{3} - 15 y$
So, the result is: $- \frac{4 y^{3}}{45} - y$
Add the constant of integration:

$- \frac{4 y^{3}}{45} - y+ \mathrm{constant}$

The answer is:

$- \frac{4 y^{3}}{45} - y+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                              
 |      2                      3
 | - 4*y  - 15              4*y 
 | ----------- dy = C - y - ----
 |      15                   45 
 |                              
/

$$\int \frac{- 4 y^{2} - 15}{15}\, dy = C - \frac{4 y^{3}}{45} - y$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

      ____
-14*\/ 15 
----------
    3

$$- \frac{14 \sqrt{15}}{3}$$

      ____
-14*\/ 15 
----------
    3

$$- \frac{14 \sqrt{15}}{3}$$

-14*sqrt(15)/3

Numerical answer [src]

-18.0739222823013

-18.0739222823013

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

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Integral of (-4*y^2-15)/15 dy

Limits of integration:

The graph:

Piecewise:

The solution