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Identical expressions
cbrt(4x- five)
cubic root of (4x minus 5)
cubic root of (4x minus five)
cbrt4x-5
cbrt(4x-5)dx
Similar expressions
cbrt(4x+5)

Integral of cbrt(4x-5) dx

The solution

You have entered [src]

  1               
  /               
 |                
 |  3 _________   
 |  \/ 4*x - 5  dx
 |                
/                 
0

$$\int\limits_{0}^{1} \sqrt[3]{4 x - 5}\, dx$$

Integral((4*x - 5)^(1/3), (x, 0, 1))

Detail solution

Let $u = 4 x - 5$ .

Then let $du = 4 dx$ and substitute $\frac{du}{4}$ :

$\int \frac{\sqrt[3]{u}}{4}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sqrt[3]{u}\, du = \frac{\int \sqrt[3]{u}\, du}{4}$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \sqrt[3]{u}\, du = \frac{3 u^{\frac{4}{3}}}{4}$
  So, the result is: $\frac{3 u^{\frac{4}{3}}}{16}$
Now substitute $u$ back in:

$\frac{3 \left(4 x - 5\right)^{\frac{4}{3}}}{16}$
Now simplify:

$\frac{3 \left(4 x - 5\right)^{\frac{4}{3}}}{16}$
Add the constant of integration:

$\frac{3 \left(4 x - 5\right)^{\frac{4}{3}}}{16}+ \mathrm{constant}$

The answer is:

$\frac{3 \left(4 x - 5\right)^{\frac{4}{3}}}{16}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   
 |                                 4/3
 | 3 _________          3*(4*x - 5)   
 | \/ 4*x - 5  dx = C + --------------
 |                            16      
/

$$\int \sqrt[3]{4 x - 5}\, dx = C + \frac{3 \left(4 x - 5\right)^{\frac{4}{3}}}{16}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    3 ____      3 ____
  3*\/ -1    15*\/ -5 
- -------- + ---------
     16          16

$$- \frac{3 \sqrt[3]{-1}}{16} + \frac{15 \sqrt[3]{-5}}{16}$$

    3 ____      3 ____
  3*\/ -1    15*\/ -5 
- -------- + ---------
     16          16

$$- \frac{3 \sqrt[3]{-1}}{16} + \frac{15 \sqrt[3]{-5}}{16}$$

-3*(-1)^(1/3)/16 + 15*(-5)^(1/3)/16

Numerical answer [src]

(0.707801225004702 + 1.22594768336763j)

(0.707801225004702 + 1.22594768336763j)

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

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Integral of cbrt(4x-5) dx

Limits of integration:

The graph:

Piecewise:

The solution