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Identical expressions
one /(cbrt(five - six *x))
1 divide by ( cubic root of (5 minus 6 multiply by x))
one divide by ( cubic root of (five minus six multiply by x))
1/(cbrt(5-6x))
1/cbrt5-6x
1 divide by (cbrt(5-6*x))
1/(cbrt(5-6*x))dx
Similar expressions
1/(cbrt(5+6*x))

Integral of 1/(cbrt(5-6*x)) dx

The solution

You have entered [src]

   1               
   /               
  |                
  |       1        
  |  ----------- dx
  |  3 _________   
  |  \/ 5 - 6*x    
  |                
 /                 
-1/2

$$\int\limits_{- \frac{1}{2}}^{1} \frac{1}{\sqrt[3]{5 - 6 x}}\, dx$$

Integral(1/((5 - 6*x)^(1/3)), (x, -1/2, 1))

Detail solution

Let $u = \sqrt[3]{5 - 6 x}$ .

Then let $du = - \frac{2 dx}{\left(5 - 6 x\right)^{\frac{2}{3}}}$ and substitute $- \frac{du}{2}$ :

$\int \left(- \frac{u}{2}\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int u\, du = - \frac{\int u\, du}{2}$
  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: $- \frac{u^{2}}{4}$
Now substitute $u$ back in:

$- \frac{\left(5 - 6 x\right)^{\frac{2}{3}}}{4}$
Add the constant of integration:

$- \frac{\left(5 - 6 x\right)^{\frac{2}{3}}}{4}+ \mathrm{constant}$

The answer is:

$- \frac{\left(5 - 6 x\right)^{\frac{2}{3}}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                 
 |                               2/3
 |      1               (5 - 6*x)   
 | ----------- dx = C - ------------
 | 3 _________               4      
 | \/ 5 - 6*x                       
 |                                  
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

        2/3
    (-1)   
1 - -------
       4

$$1 - \frac{\left(-1\right)^{\frac{2}{3}}}{4}$$

        2/3
    (-1)   
1 - -------
       4

$$1 - \frac{\left(-1\right)^{\frac{2}{3}}}{4}$$

1 - (-1)^(2/3)/4

Numerical answer [src]

(1.11370031232512 - 0.223516945168406j)

(1.11370031232512 - 0.223516945168406j)

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

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Identical expressions

Similar expressions

Integral of 1/(cbrt(5-6*x)) dx

Limits of integration:

The graph:

Piecewise:

The solution