Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^2/(x-2)
Integral of x(1-x)^1/2
Integral of sqrt(1+1/(x^2))
Integral of sin(x)*dx/(1+3*cos(x))
Identical expressions
(one)/(\root(three)(x))- two \root(three)(x)
(1) divide by (\root(3)(x)) minus 2\root(3)(x)
(one) divide by (\root(three)(x)) minus two \root(three)(x)
1/\root3x-2\root3x
(1) divide by (\root(3)(x))-2\root(3)(x)
(1)/(\root(3)(x))-2\root(3)(x)dx
Similar expressions
(1)/(\root(3)(x))+2\root(3)(x)

Solving integrals/ (1)/(\root(3)(x))-2\root(3)(x)

Integral of (1)/(\root(3)(x))-2\root(3)(x) dx

The solution

You have entered [src]

 27                       
  /                       
 |                        
 |  /   1        2    \   
 |  |------- - -----*x| dx
 |  |  ___       ___  |   
 |  \\/ 3 *x   \/ 3   /   
 |                        
/                         
8

$$\int\limits_{8}^{27} \left(- x \frac{2}{\sqrt{3}} + \frac{1}{\sqrt{3} x}\right)\, dx$$

Integral(1/(sqrt(3)*x) - 2/sqrt(3)*x, (x, 8, 27))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x \frac{2}{\sqrt{3}}\right)\, dx = - \frac{2 \sqrt{3} \int x\, dx}{3}$
  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: $- \frac{\sqrt{3} x^{2}}{3}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{\sqrt{3} \log{\left(x \right)}}{3}$
The result is: $- \frac{\sqrt{3} x^{2}}{3} + \frac{\sqrt{3} \log{\left(x \right)}}{3}$
Now simplify:

$\frac{\sqrt{3} \left(- x^{2} + \log{\left(x \right)}\right)}{3}$
Add the constant of integration:

$\frac{\sqrt{3} \left(- x^{2} + \log{\left(x \right)}\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{\sqrt{3} \left(- x^{2} + \log{\left(x \right)}\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                    
 |                                ___  2     ___       
 | /   1        2    \          \/ 3 *x    \/ 3 *log(x)
 | |------- - -----*x| dx = C - -------- + ------------
 | |  ___       ___  |             3            3      
 | \\/ 3 *x   \/ 3   /                                 
 |                                                     
/

$$\int \left(- x \frac{2}{\sqrt{3}} + \frac{1}{\sqrt{3} x}\right)\, dx = C - \frac{\sqrt{3} x^{2}}{3} + \frac{\sqrt{3} \log{\left(x \right)}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

        ___     ___            ___        
  665*\/ 3    \/ 3 *log(8)   \/ 3 *log(27)
- --------- - ------------ + -------------
      3            3               3

$$- \frac{665 \sqrt{3}}{3} - \frac{\sqrt{3} \log{\left(8 \right)}}{3} + \frac{\sqrt{3} \log{\left(27 \right)}}{3}$$

        ___     ___            ___        
  665*\/ 3    \/ 3 *log(8)   \/ 3 *log(27)
- --------- - ------------ + -------------
      3            3               3

$$- \frac{665 \sqrt{3}}{3} - \frac{\sqrt{3} \log{\left(8 \right)}}{3} + \frac{\sqrt{3} \log{\left(27 \right)}}{3}$$

-665*sqrt(3)/3 - sqrt(3)*log(8)/3 + sqrt(3)*log(27)/3

Numerical answer [src]

-383.235642843161

-383.235642843161

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (1)/(\root(3)(x))-2\root(3)(x) dx

Limits of integration:

The graph:

Piecewise:

The solution