Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of √xdx
Integral of √(1-x^2)
Integral of 1/(2x)
Integral of (e^x)/x
Identical expressions
(8x- five /x^ six + seven √x)
(8x minus 5 divide by x to the power of 6 plus 7√x)
(8x minus five divide by x to the power of six plus seven √x)
(8x-5/x6+7√x)
8x-5/x6+7√x
(8x-5/x⁶+7√x)
8x-5/x^6+7√x
(8x-5 divide by x^6+7√x)
(8x-5/x^6+7√x)dx
Similar expressions
(8x-5/x^6-7√x)
(8x+5/x^6+7√x)

Integral of (8x-5/x^6+7√x) dx

The solution

You have entered [src]

  1                        
  /                        
 |                         
 |  /      5        ___\   
 |  |8*x - -- + 7*\/ x | dx
 |  |       6          |   
 |  \      x           /   
 |                         
/                          
0

$$\int\limits_{0}^{1} \left(7 \sqrt{x} + \left(8 x - \frac{5}{x^{6}}\right)\right)\, dx$$

Integral(8*x - 5/x^6 + 7*sqrt(x), (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:
  
  $\int 7 \sqrt{x}\, dx = 7 \int \sqrt{x}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \sqrt{x}\, dx = \frac{2 x^{\frac{3}{2}}}{3}$
  So, the result is: $\frac{14 x^{\frac{3}{2}}}{3}$
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:
    
    $\int \left(- \frac{5}{x^{6}}\right)\, dx = - 5 \int \frac{1}{x^{6}}\, dx$
    1. Don't know the steps in finding this integral.
      
      But the integral is
      
      $- \frac{1}{5 x^{5}}$
    So, the result is: $\frac{1}{x^{5}}$
  The result is: $4 x^{2} + \frac{1}{x^{5}}$
The result is: $\frac{14 x^{\frac{3}{2}}}{3} + 4 x^{2} + \frac{1}{x^{5}}$
Now simplify:

$\frac{14 x^{\frac{13}{2}} + 12 x^{7} + 3}{3 x^{5}}$
Add the constant of integration:

$\frac{14 x^{\frac{13}{2}} + 12 x^{7} + 3}{3 x^{5}}+ \mathrm{constant}$

The answer is:

$\frac{14 x^{\frac{13}{2}} + 12 x^{7} + 3}{3 x^{5}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                 
 |                                               3/2
 | /      5        ___\          1       2   14*x   
 | |8*x - -- + 7*\/ x | dx = C + -- + 4*x  + -------
 | |       6          |           5             3   
 | \      x           /          x                  
 |                                                  
/

$$\int \left(7 \sqrt{x} + \left(8 x - \frac{5}{x^{6}}\right)\right)\, dx = C + \frac{14 x^{\frac{3}{2}}}{3} + 4 x^{2} + \frac{1}{x^{5}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-oo

$$-\infty$$

-oo

$$-\infty$$

-oo

Numerical answer [src]

-3.5055375951983e+95

-3.5055375951983e+95

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (8x-5/x^6+7√x) dx

Limits of integration:

The graph:

Piecewise:

The solution