Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 1/sqrt(1+u^2)
Integral of (2x+3)
Integral of 1-7*x^2
Integral of (x-1)/x^3
Identical expressions
one /(3x- two)^(one / five)
1 divide by (3x minus 2) to the power of (1 divide by 5)
one divide by (3x minus two) to the power of (one divide by five)
1/(3x-2)(1/5)
1/3x-21/5
1/3x-2^1/5
1 divide by (3x-2)^(1 divide by 5)
1/(3x-2)^(1/5)dx
Similar expressions
1/(3x+2)^(1/5)

Integral of 1/(3x-2)^(1/5) dx

The solution

You have entered [src]

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

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

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

Detail solution

Let $u = \sqrt[5]{3 x - 2}$ .

Then let $du = \frac{3 dx}{5 \left(3 x - 2\right)^{\frac{4}{5}}}$ and substitute $\frac{5 du}{3}$ :

$\int \frac{5 u^{3}}{3}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int u^{3}\, du = \frac{5 \int u^{3}\, du}{3}$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int u^{3}\, du = \frac{u^{4}}{4}$
  So, the result is: $\frac{5 u^{4}}{12}$
Now substitute $u$ back in:

$\frac{5 \left(3 x - 2\right)^{\frac{4}{5}}}{12}$
Now simplify:

$\frac{5 \left(3 x - 2\right)^{\frac{4}{5}}}{12}$
Add the constant of integration:

$\frac{5 \left(3 x - 2\right)^{\frac{4}{5}}}{12}+ \mathrm{constant}$

The answer is:

$\frac{5 \left(3 x - 2\right)^{\frac{4}{5}}}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   
 |                                 4/5
 |      1               5*(3*x - 2)   
 | ----------- dx = C + --------------
 | 5 _________                12      
 | \/ 3*x - 2                         
 |                                    
/

$$\int \frac{1}{\sqrt[5]{3 x - 2}}\, dx = C + \frac{5 \left(3 x - 2\right)^{\frac{4}{5}}}{12}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

5           /    4/5\
-- - oo*sign\(-3)   /
12

$$\frac{5}{12} - \infty \operatorname{sign}{\left(\left(-3\right)^{\frac{4}{5}} \right)}$$

5           /    4/5\
-- - oo*sign\(-3)   /
12

$$\frac{5}{12} - \infty \operatorname{sign}{\left(\left(-3\right)^{\frac{4}{5}} \right)}$$

5/12 - oo*sign((-3)^(4/5))

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 1/(3x-2)^(1/5) dx

Limits of integration:

The graph:

Piecewise:

The solution