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Identical expressions
x^ two *e1-2xdx
x squared multiply by e1 minus 2xdx
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Similar expressions
x^2*e1+2xdx

Integral of x^2*e1-2xdx dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |  / 2         \   
 |  \x *e1 - 2*x/ dx
 |                  
/                   
0

$$\int\limits_{0}^{1} \left(e_{1} x^{2} - 2 x\right)\, dx$$

Integral(x^2*e1 - 2*x, (x, 0, 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:
  
  $\int e_{1} x^{2}\, dx = e_{1} \int x^{2}\, dx$
  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: $\frac{e_{1} x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 2 x\right)\, dx = - 2 \int x\, dx$
  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: $- x^{2}$
The result is: $\frac{e_{1} x^{3}}{3} - x^{2}$
Now simplify:

$\frac{x^{2} \left(e_{1} x - 3\right)}{3}$
Add the constant of integration:

$\frac{x^{2} \left(e_{1} x - 3\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(e_{1} x - 3\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                 
 |                                 3
 | / 2         \           2   e1*x 
 | \x *e1 - 2*x/ dx = C - x  + -----
 |                               3  
/

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

Simplify

The answer [src]

     e1
-1 + --
     3

$$\frac{e_{1}}{3} - 1$$

     e1
-1 + --
     3

$$\frac{e_{1}}{3} - 1$$

-1 + e1/3

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

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Integral of x^2*e1-2xdx dx

Limits of integration:

The graph:

Piecewise:

The solution