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Similar expressions
dx/cbrt(x+1)3

Integral of dx/cbrt(x-1)3 dx

The solution

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  2             
  /             
 |              
 |      3       
 |  --------- dx
 |  3 _______   
 |  \/ x - 1    
 |              
/               
1

$$\int\limits_{1}^{2} \frac{3}{\sqrt[3]{x - 1}}\, dx$$

Integral(3/(x - 1)^(1/3), (x, 1, 2))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{3}{\sqrt[3]{x - 1}}\, dx = 3 \int \frac{1}{\sqrt[3]{x - 1}}\, dx$
1. Let $u = \sqrt[3]{x - 1}$ .
  
  Then let $du = \frac{dx}{3 \left(x - 1\right)^{\frac{2}{3}}}$ and substitute $3 du$ :
  
  $\int 3 u\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int u\, du = 3 \int u\, du$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u\, du = \frac{u^{2}}{2}$
    So, the result is: $\frac{3 u^{2}}{2}$
  Now substitute $u$ back in:
  
  $\frac{3 \left(x - 1\right)^{\frac{2}{3}}}{2}$
So, the result is: $\frac{9 \left(x - 1\right)^{\frac{2}{3}}}{2}$
Now simplify:

$\frac{9 \left(x - 1\right)^{\frac{2}{3}}}{2}$
Add the constant of integration:

$\frac{9 \left(x - 1\right)^{\frac{2}{3}}}{2}+ \mathrm{constant}$

The answer is:

$\frac{9 \left(x - 1\right)^{\frac{2}{3}}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                             2/3
 |     3              9*(x - 1)   
 | --------- dx = C + ------------
 | 3 _______               2      
 | \/ x - 1                       
 |                                
/

$$\int \frac{3}{\sqrt[3]{x - 1}}\, dx = C + \frac{9 \left(x - 1\right)^{\frac{2}{3}}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

9/2

$$\frac{9}{2}$$

9/2

$$\frac{9}{2}$$

9/2

Numerical answer [src]

4.49999999999907

4.49999999999907

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

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Integral of dx/cbrt(x-1)3 dx

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The solution