Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of sin(5x)
Integral of sqrt(1+x^2)/x
Integral of t^2
Integral of (x-1)^1/2
Identical expressions
(three /sqrt(x))+ four /(x^ eight)
(3 divide by square root of (x)) plus 4 divide by (x to the power of 8)
(three divide by square root of (x)) plus four divide by (x to the power of eight)
(3/√(x))+4/(x^8)
(3/sqrt(x))+4/(x8)
3/sqrtx+4/x8
(3/sqrt(x))+4/(x⁸)
3/sqrtx+4/x^8
(3 divide by sqrt(x))+4 divide by (x^8)
(3/sqrt(x))+4/(x^8)dx
Similar expressions
(3/sqrt(x))-4/(x^8)

Integral of (3/sqrt(x))+4/(x^8) dx

The solution

You have entered [src]

  1                
  /                
 |                 
 |  /  3     4 \   
 |  |----- + --| dx
 |  |  ___    8|   
 |  \\/ x    x /   
 |                 
/                  
0

$$\int\limits_{0}^{1} \left(\frac{4}{x^{8}} + \frac{3}{\sqrt{x}}\right)\, dx$$

Integral(3/sqrt(x) + 4/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:
  
  $\int \frac{4}{x^{8}}\, dx = 4 \int \frac{1}{x^{8}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- \frac{1}{7 x^{7}}$
  So, the result is: $- \frac{4}{7 x^{7}}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{3}{\sqrt{x}}\, dx = 3 \int \frac{1}{\sqrt{x}}\, dx$
  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: $6 \sqrt{x}$
The result is: $6 \sqrt{x} - \frac{4}{7 x^{7}}$
Now simplify:

$\frac{2 \left(21 x^{\frac{15}{2}} - 2\right)}{7 x^{7}}$
Add the constant of integration:

$\frac{2 \left(21 x^{\frac{15}{2}} - 2\right)}{7 x^{7}}+ \mathrm{constant}$

The answer is:

$\frac{2 \left(21 x^{\frac{15}{2}} - 2\right)}{7 x^{7}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                    
 |                                     
 | /  3     4 \              ___    4  
 | |----- + --| dx = C + 6*\/ x  - ----
 | |  ___    8|                       7
 | \\/ x    x /                    7*x 
 |                                     
/

$$\int \left(\frac{4}{x^{8}} + \frac{3}{\sqrt{x}}\right)\, dx = C + 6 \sqrt{x} - \frac{4}{7 x^{7}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

2.72353730166202e+133

2.72353730166202e+133

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (3/sqrt(x))+4/(x^8) dx

Limits of integration:

The graph:

Piecewise:

The solution