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Solving integrals/ cbrt(x+1)

Integral of cbrt(x+1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  5             
  /             
 |              
 |  3 _______   
 |  \/ x + 1  dx
 |              
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1
∫15x+13 dx\int\limits_{1}^{5} \sqrt[3]{x + 1}\, dx 
Integral((x + 1)^(1/3), (x, 1, 5))
Detail solution

  1. Let u=x+1u = x + 1.

    Then let du=dxdu = dx and substitute dudu:

    ∫u3 du\int \sqrt[3]{u}\, du

    1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫u3 du=3u434\int \sqrt[3]{u}\, du = \frac{3 u^{\frac{4}{3}}}{4}

    Now substitute uu back in:

    3(x+1)434\frac{3 \left(x + 1\right)^{\frac{4}{3}}}{4}

  2. Now simplify:

    3(x+1)434\frac{3 \left(x + 1\right)^{\frac{4}{3}}}{4}

  3. Add the constant of integration:

    3(x+1)434+constant\frac{3 \left(x + 1\right)^{\frac{4}{3}}}{4}+ \mathrm{constant}

The answer is:

3(x+1)434+constant\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      
/
∫x+13 dx=C+3(x+1)434\int \sqrt[3]{x + 1}\, dx = C + \frac{3 \left(x + 1\right)^{\frac{4}{3}}}{4}
Simplify
The graph
1.05.01.52.02.53.03.54.04.5010
Plot the graph f(x)
The answer [src] 
    3 ___     3 ___
  3*\/ 2    9*\/ 6 
- ------- + -------
     2         2
−3232+9632- \frac{3 \sqrt[3]{2}}{2} + \frac{9 \sqrt[3]{6}}{2} 
=
= 
    3 ___     3 ___
  3*\/ 2    9*\/ 6 
- ------- + -------
     2         2
−3232+9632- \frac{3 \sqrt[3]{2}}{2} + \frac{9 \sqrt[3]{6}}{2} 
-3*2^(1/3)/2 + 9*6^(1/3)/2
Numerical answer [src] 
6.28716109290232
6.28716109290232

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

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