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Identical expressions
xarcsinx/√ one -x²
xarc sinus of x divide by √1 minus x²
xarc sinus of x divide by √ one minus x²
xarcsinx divide by √1-x²
xarcsinx/√1-x²dx
Similar expressions
xarcsinx/√1+x²
xarcsinx/(√(1-x²))

Solving integrals/ xarcsinx/√1-x²

Integral of xarcsinx/√1-x² dx

The solution

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  1                    
  /                    
 |                     
 |  /x*asin(x)    2\   
 |  |--------- - x | dx
 |  |    ___       |   
 |  \  \/ 1        /   
 |                     
/                      
0

$$\int\limits_{0}^{1} \left(- x^{2} + \frac{x \operatorname{asin}{\left(x \right)}}{\sqrt{1}}\right)\, dx$$

Integral((x*asin(x))/sqrt(1) - x^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $- \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{x \operatorname{asin}{\left(x \right)}}{\sqrt{1}}\, dx = \int x \operatorname{asin}{\left(x \right)}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $\frac{x^{2} \operatorname{asin}{\left(x \right)}}{2} + \frac{x \sqrt{1 - x^{2}}}{4} - \frac{\operatorname{asin}{\left(x \right)}}{4}$
  So, the result is: $\frac{x^{2} \operatorname{asin}{\left(x \right)}}{2} + \frac{x \sqrt{1 - x^{2}}}{4} - \frac{\operatorname{asin}{\left(x \right)}}{4}$
The result is: $- \frac{x^{3}}{3} + \frac{x^{2} \operatorname{asin}{\left(x \right)}}{2} + \frac{x \sqrt{1 - x^{2}}}{4} - \frac{\operatorname{asin}{\left(x \right)}}{4}$
Add the constant of integration:

$- \frac{x^{3}}{3} + \frac{x^{2} \operatorname{asin}{\left(x \right)}}{2} + \frac{x \sqrt{1 - x^{2}}}{4} - \frac{\operatorname{asin}{\left(x \right)}}{4}+ \mathrm{constant}$

The answer is:

$- \frac{x^{3}}{3} + \frac{x^{2} \operatorname{asin}{\left(x \right)}}{2} + \frac{x \sqrt{1 - x^{2}}}{4} - \frac{\operatorname{asin}{\left(x \right)}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                           ________
 |                            3              2               /      2 
 | /x*asin(x)    2\          x    asin(x)   x *asin(x)   x*\/  1 - x  
 | |--------- - x | dx = C - -- - ------- + ---------- + -------------
 | |    ___       |          3       4          2              4      
 | \  \/ 1        /                                                   
 |                                                                    
/

$$\int \left(- x^{2} + \frac{x \operatorname{asin}{\left(x \right)}}{\sqrt{1}}\right)\, dx = C - \frac{x^{3}}{3} + \frac{x^{2} \operatorname{asin}{\left(x \right)}}{2} + \frac{x \sqrt{1 - x^{2}}}{4} - \frac{\operatorname{asin}{\left(x \right)}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  1   pi
- - + --
  3   8

$$- \frac{1}{3} + \frac{\pi}{8}$$

  1   pi
- - + --
  3   8

$$- \frac{1}{3} + \frac{\pi}{8}$$

-1/3 + pi/8

Numerical answer [src]

0.0593657483653908

0.0593657483653908

The graph

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

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Integral of xarcsinx/√1-x² dx

Limits of integration:

The graph:

Piecewise:

The solution