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Integral of 1/(2-x)
Identical expressions
x^ two +5x- fourteen
x squared plus 5x minus 14
x to the power of two plus 5x minus fourteen
x2+5x-14
x²+5x-14
x to the power of 2+5x-14
x^2+5x-14dx
Similar expressions
x^2+5x+14
x^2-5x-14

Integral of x^2+5x-14 dx

The solution

You have entered [src]

 27                   
 --                   
 10                   
  /                   
 |                    
 |  / 2           \   
 |  \x  + 5*x - 14/ dx
 |                    
/                     
23                    
--                    
10

$$\int\limits_{\frac{23}{10}}^{\frac{27}{10}} \left(\left(x^{2} + 5 x\right) - 14\right)\, dx$$

Integral(x^2 + 5*x - 14, (x, 23/10, 27/10))

Detail solution

Integrate term-by-term:
1. 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:
    
    $\int 5 x\, dx = 5 \int x\, dx$
    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: $\frac{x^{3}}{3} + \frac{5 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-14\right)\, dx = - 14 x$
The result is: $\frac{x^{3}}{3} + \frac{5 x^{2}}{2} - 14 x$
Now simplify:

$\frac{x \left(2 x^{2} + 15 x - 84\right)}{6}$
Add the constant of integration:

$\frac{x \left(2 x^{2} + 15 x - 84\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} + 15 x - 84\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                  3      2
 | / 2           \                 x    5*x 
 | \x  + 5*x - 14/ dx = C - 14*x + -- + ----
 |                                 3     2  
/

$$\int \left(\left(x^{2} + 5 x\right) - 14\right)\, dx = C + \frac{x^{3}}{3} + \frac{5 x^{2}}{2} - 14 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1429
----
750

$$\frac{1429}{750}$$

1429
----
750

$$\frac{1429}{750}$$

1429/750

Numerical answer [src]

1.90533333333334

1.90533333333334

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

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Integral of x^2+5x-14 dx

Limits of integration:

The graph:

Piecewise:

The solution