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(5-x)^(1/3)
Solving integrals/ (5-x)^(1/3)

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

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src] 
  2             
  /             
 |              
 |  3 _______   
 |  \/ 5 - x  dx
 |              
/               
1
$$\int\limits_{1}^{2} \sqrt[3]{5 - x}\, dx$$ 
Integral((5 - x)^(1/3), (x, 1, 2))
Detail solution

  1. Let .

    Then let and substitute :

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is when :

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                               
 |                             4/3
 | 3 _______          3*(5 - x)   
 | \/ 5 - x  dx = C - ------------
 |                         4      
/
$$\int \sqrt[3]{5 - x}\, dx = C - \frac{3 \left(5 - x\right)^{\frac{4}{3}}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
           3 ___
   2/3   9*\/ 3 
3*2    - -------
            4
$$- \frac{9 \sqrt[3]{3}}{4} + 3 \cdot 2^{\frac{2}{3}}$$ 
=
= 
           3 ___
   2/3   9*\/ 3 
3*2    - -------
            4
$$- \frac{9 \sqrt[3]{3}}{4} + 3 \cdot 2^{\frac{2}{3}}$$ 
3*2^(2/3) - 9*3^(1/3)/4
Numerical answer [src] 
1.51714162271293
1.51714162271293
The graph
Integral of (5-x)^(1/3) dx

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

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