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Identical expressions
four /sqrtx- one /x^ eight
4 divide by square root of x minus 1 divide by x to the power of 8
four divide by square root of x minus one divide by x to the power of eight
4/√x-1/x^8
4/sqrtx-1/x8
4/sqrtx-1/x⁸
4 divide by sqrtx-1 divide by x^8
4/sqrtx-1/x^8dx
Similar expressions
4/sqrtx+1/x^8

Integral of 4/sqrtx-1/x^8 dx

The solution

You have entered [src]

  1                
  /                
 |                 
 |  /  4     1 \   
 |  |----- - --| dx
 |  |  ___    8|   
 |  \\/ x    x /   
 |                 
/                  
0

$$\int\limits_{0}^{1} \left(- \frac{1}{x^{8}} + \frac{4}{\sqrt{x}}\right)\, dx$$

Integral(4/sqrt(x) - 1/x^8, (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:
  
  $\int \left(- \frac{1}{x^{8}}\right)\, dx = - \int \frac{1}{x^{8}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- \frac{1}{7 x^{7}}$
  So, the result is: $\frac{1}{7 x^{7}}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{4}{\sqrt{x}}\, dx = 4 \int \frac{1}{\sqrt{x}}\, dx$
  1. Let $u = \sqrt{x}$ .
    
    Then let $du = \frac{dx}{2 \sqrt{x}}$ and substitute $2 du$ :
    
    $\int 2\, du$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\text{False}$
      1. The integral of a constant is the constant times the variable of integration:
        
        $\int 1\, du = u$
      So, the result is: $2 u$
    Now substitute $u$ back in:
    
    $2 \sqrt{x}$
  So, the result is: $8 \sqrt{x}$
The result is: $8 \sqrt{x} + \frac{1}{7 x^{7}}$
Now simplify:

$\frac{56 x^{\frac{15}{2}} + 1}{7 x^{7}}$
Add the constant of integration:

$\frac{56 x^{\frac{15}{2}} + 1}{7 x^{7}}+ \mathrm{constant}$

The answer is:

$\frac{56 x^{\frac{15}{2}} + 1}{7 x^{7}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                    
 |                                     
 | /  4     1 \              ___    1  
 | |----- - --| dx = C + 8*\/ x  + ----
 | |  ___    8|                       7
 | \\/ x    x /                    7*x 
 |                                     
/

$$\int \left(- \frac{1}{x^{8}} + \frac{4}{\sqrt{x}}\right)\, dx = C + 8 \sqrt{x} + \frac{1}{7 x^{7}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-oo

$$-\infty$$

-oo

$$-\infty$$

-oo

Numerical answer [src]

-6.80884325415506e+132

-6.80884325415506e+132

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

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Integral of 4/sqrtx-1/x^8 dx

Limits of integration:

The graph:

Piecewise:

The solution