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three x-3/√ one -x²dx
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3x-3/√1+x²dx
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Integral of 3x-3/√1-x²dx dx

The solution

You have entered [src]

  1                      
  /                      
 |                       
 |  /        3      2\   
 |  |3*x - ----- - x | dx
 |  |        ___     |   
 |  \      \/ 1      /   
 |                       
/                        
0

$$\int\limits_{0}^{1} \left(- x^{2} + \left(3 x - \frac{3}{\sqrt{1}}\right)\right)\, dx$$

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

$\frac{x \left(- 2 x^{2} + 9 x - 18\right)}{6}$
Add the constant of integration:

$\frac{x \left(- 2 x^{2} + 9 x - 18\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- 2 x^{2} + 9 x - 18\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-11/6

$$- \frac{11}{6}$$

-11/6

$$- \frac{11}{6}$$

-11/6

Numerical answer [src]

-1.83333333333333

-1.83333333333333

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

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Integral of 3x-3/√1-x²dx dx

Limits of integration:

The graph:

Piecewise:

The solution