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Identical expressions
(6x^- nineteen +8x- one)
(6x to the power of minus 19 plus 8x minus 1)
(6x to the power of minus nineteen plus 8x minus one)
(6x-19+8x-1)
6x-19+8x-1
6x^-19+8x-1
(6x^-19+8x-1)dx
Similar expressions
(6x^-19-8x-1)
(6x^-19+8x+1)
(6x^+19+8x-1)

Solving integrals/ (6x^-19+8x-1)

Integral of (6x^-19+8x-1) dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  / 6           \   
 |  |--- + 8*x - 1| dx
 |  | 19          |   
 |  \x            /   
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(\left(8 x + \frac{6}{x^{19}}\right) - 1\right)\, dx$$

Integral(6/x^19 + 8*x - 1, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 8 x\, dx = 8 \int x\, dx$
    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: $4 x^{2}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{6}{x^{19}}\, dx = 6 \int \frac{1}{x^{19}}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int \frac{1}{x^{19}}\, dx = - \frac{1}{18 x^{18}}$
    So, the result is: $- \frac{1}{3 x^{18}}$
  The result is: $4 x^{2} - \frac{1}{3 x^{18}}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-1\right)\, dx = - x$
The result is: $4 x^{2} - x - \frac{1}{3 x^{18}}$
Add the constant of integration:

$4 x^{2} - x - \frac{1}{3 x^{18}}+ \mathrm{constant}$

The answer is:

$4 x^{2} - x - \frac{1}{3 x^{18}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                          
 | / 6           \                 2     1  
 | |--- + 8*x - 1| dx = C - x + 4*x  - -----
 | | 19          |                        18
 | \x            /                     3*x  
 |                                          
/

$$\int \left(\left(8 x + \frac{6}{x^{19}}\right) - 1\right)\, dx = C + 4 x^{2} - x - \frac{1}{3 x^{18}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

3.95648477912341e+342

3.95648477912341e+342

The graph

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

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Integral of (6x^-19+8x-1) dx

Limits of integration:

The graph:

Piecewise:

The solution