Mister Exam

Other calculators

  • How to use it?

  • Integral of d{x}:
  • Integral of 1/(x*(1-x)) Integral of 1/(x*(1-x))
  • Integral of (x^3+1)^1/2 Integral of (x^3+1)^1/2
  • Integral of (x^2) Integral of (x^2)
  • Integral of (x^2+2x) Integral of (x^2+2x)

  • Identical expressions

  • x^(two *dx)/sqrt(one -x^ three)
  • x to the power of (2 multiply by dx) divide by square root of (1 minus x cubed )
  • x to the power of (two multiply by dx) divide by square root of (one minus x to the power of three)
  • x^(2*dx)/√(1-x^3)
  • x(2*dx)/sqrt(1-x3)
  • x2*dx/sqrt1-x3
  • x^(2*dx)/sqrt(1-x³)
  • x to the power of (2*dx)/sqrt(1-x to the power of 3)
  • x^(2dx)/sqrt(1-x^3)
  • x(2dx)/sqrt(1-x3)
  • x2dx/sqrt1-x3
  • x^2dx/sqrt1-x^3
  • x^(2*dx) divide by sqrt(1-x^3)

  • Similar expressions

  • x^(2*dx)/sqrt(1+x^3)
Solving integrals/ x^(2*dx)/sqrt(1-x^3)

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |        2       
 |       x        
 |  ----------- dx
 |     ________   
 |    /      3    
 |  \/  1 - x     
 |                
/                 
0
$$\int\limits_{0}^{1} \frac{x^{2}}{\sqrt{1 - x^{3}}}\, dx$$ 
Integral(x^2/sqrt(1 - x^3), (x, 0, 1))
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 a constant is the constant times the variable of integration:

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                  
 |                           ________
 |       2                  /      3 
 |      x               2*\/  1 - x  
 | ----------- dx = C - -------------
 |    ________                3      
 |   /      3                        
 | \/  1 - x                         
 |                                   
/
$$\int \frac{x^{2}}{\sqrt{1 - x^{3}}}\, dx = C - \frac{2 \sqrt{1 - x^{3}}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
2/3
$$\frac{2}{3}$$ 
=
= 
2/3
$$\frac{2}{3}$$ 
2/3
Numerical answer [src] 
0.666666666279959
0.666666666279959

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

    © Mister Exam – Calculator