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Identical expressions
(x^ two +2x+ one -(x+ seven))
(x squared plus 2x plus 1 minus (x plus 7))
(x to the power of two plus 2x plus one minus (x plus seven))
(x2+2x+1-(x+7))
x2+2x+1-x+7
(x²+2x+1-(x+7))
(x to the power of 2+2x+1-(x+7))
x^2+2x+1-x+7
(x^2+2x+1-(x+7))dx
Similar expressions
(x^2+2x+1-(x-7))
(x^2-2x+1-(x+7))
(x^2+2x-1-(x+7))
(x^2+2x+1+(x+7))

Solving integrals/ (x^2+2x+1-(x+7))

Integral of (x^2+2x+1-(x+7)) dx

The solution

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  2                            
  /                            
 |                             
 |  / 2                    \   
 |  \x  + 2*x + 1 - (x + 7)/ dx
 |                             
/                              
-3

$$\int\limits_{-3}^{2} \left(x^{2} + 2 x - \left(x + 7\right) + 1\right)\, dx$$

Integral(x^2 + 2*x + 1 - (x + 7), (x, -3, 2))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 x\, dx = 2 \int x\, dx$
  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: $x^{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- (x + 7)\right)\, dx = - \int \left(x + 7\right)\, dx$
  1. Integrate term-by-term:
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x\, dx = \frac{x^{2}}{2}$
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int 7\, dx = 7 x$
    The result is: $\frac{x^{2}}{2} + 7 x$
  So, the result is: $- \frac{x^{2}}{2} - 7 x$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $\frac{x^{3}}{3} + \frac{x^{2}}{2} - 6 x$
Now simplify:

$\frac{x \left(2 x^{2} + 3 x - 36\right)}{6}$
Add the constant of integration:

$\frac{x \left(2 x^{2} + 3 x - 36\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} + 3 x - 36\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                               
 |                                    2          3
 | / 2                    \          x          x 
 | \x  + 2*x + 1 - (x + 7)/ dx = C + -- - 6*x + --
 |                                   2          3 
/

$${{x^3}\over{3}}+{{x^2}\over{2}}-6\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-125/6

$$-{{125}\over{6}}$$

-125/6

$$- \frac{125}{6}$$

Упростить

Numerical answer [src]

-20.8333333333333

-20.8333333333333

The graph

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

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Similar expressions

Integral of (x^2+2x+1-(x+7)) dx

Limits of integration:

The graph:

Piecewise:

The solution