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Derivative of:
(x+1)^1/3
Identical expressions
(x+ one)^ one / three
(x plus 1) to the power of 1 divide by 3
(x plus one) to the power of one divide by three
(x+1)1/3
x+11/3
x+1^1/3
(x+1)^1 divide by 3
(x+1)^1/3dx
Similar expressions
1/((x+1)^(1/3)+1)
((ln(3x+1))^(1/3))/(3x+1)
(x-7)(x+1)^(1/3)
(x-1)^1/3

Solving integrals/ (x+1)^1/3

Integral of (x+1)^1/3 dx

The solution

You have entered [src]

  1             
  /             
 |              
 |  3 _______   
 |  \/ x + 1  dx
 |              
/               
0

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

Integral((x + 1)^(1/3), (x, 0, 1))

Detail solution

Let $u = x + 1$ .

Then let $du = dx$ and substitute $du$ :

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

$\frac{3 \left(x + 1\right)^{\frac{4}{3}}}{4}$
Now simplify:

$\frac{3 \left(x + 1\right)^{\frac{4}{3}}}{4}$
Add the constant of integration:

$\frac{3 \left(x + 1\right)^{\frac{4}{3}}}{4}+ \mathrm{constant}$

The answer is:

$\frac{3 \left(x + 1\right)^{\frac{4}{3}}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                             4/3
 | 3 _______          3*(x + 1)   
 | \/ x + 1  dx = C + ------------
 |                         4      
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

        3 ___
  3   3*\/ 2 
- - + -------
  4      2

$$- \frac{3}{4} + \frac{3 \sqrt[3]{2}}{2}$$

        3 ___
  3   3*\/ 2 
- - + -------
  4      2

$$- \frac{3}{4} + \frac{3 \sqrt[3]{2}}{2}$$

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

Numerical answer [src]

1.13988157484231

1.13988157484231

The graph

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

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Identical expressions

Similar expressions

Integral of (x+1)^1/3 dx

Limits of integration:

The graph:

Piecewise:

The solution