Mister Exam

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sqrt3(x- one)^ two
square root of 3(x minus 1) squared
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Similar expressions
sqrt3(x+1)^2

Integral of sqrt3(x-1)^2 dx

The solution

You have entered [src]

  9                               
  /                               
 |                                
 |                            2   
 |  /       0.333333333333333\    
 |  \(x - 1)                 /  dx
 |                                
/                                 
2

$$\int\limits_{2}^{9} \left(\left(x - 1\right)^{0.333333333333333}\right)^{2}\, dx$$

Integral(((x - 1)^0.333333333333333)^2, (x, 2, 9))

Detail solution

Let $u = \left(x - 1\right)^{0.333333333333333}$ .

Then let $du = \frac{0.333333333333333 dx}{\left(x - 1\right)^{0.666666666666667}}$ and substitute $3.0 du$ :

$\int 3.0 u^{4.0}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int u^{4.0}\, du = 3.0 \int u^{4.0}\, du$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int u^{4.0}\, du = 0.2 u^{5.0}$
  So, the result is: $0.6 u^{5.0}$
Now substitute $u$ back in:

$0.6 \left(x - 1\right)^{1.66666666666667}$
Now simplify:

$0.6 \left(x - 1\right)^{1.66666666666667}$
Add the constant of integration:

$0.6 \left(x - 1\right)^{1.66666666666667}+ \mathrm{constant}$

The answer is:

$0.6 \left(x - 1\right)^{1.66666666666667}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                
 |                                                                 
 |                           2                                     
 | /       0.333333333333333\                      1.66666666666667
 | \(x - 1)                 /  dx = C + 0.6*(x - 1)                
 |                                                                 
/

$$\int \left(\left(x - 1\right)^{0.333333333333333}\right)^{2}\, dx = C + 0.6 \left(x - 1\right)^{1.66666666666667}$$

Simplify

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The answer [src]

18.6000000000000

$$18.6$$

18.6000000000000

$$18.6$$

18.6000000000000

Numerical answer [src]

18.6

18.6

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

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Integral of sqrt3(x-1)^2 dx

Limits of integration:

The graph:

Piecewise:

The solution