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Identical expressions
(arcsin^ two x)/sprt1-x^2
(arc sinus of squared x) divide by sprt1 minus x squared
(arc sinus of to the power of two x) divide by sprt1 minus x squared
(arcsin2x)/sprt1-x2
arcsin2x/sprt1-x2
(arcsin²x)/sprt1-x²
(arcsin to the power of 2x)/sprt1-x to the power of 2
arcsin^2x/sprt1-x^2
(arcsin^2x) divide by sprt1-x^2
(arcsin^2x)/sprt1-x^2dx
Similar expressions
(arcsin^2x)/sprt1+x^2

Solving integrals/ (arcsin^2x)/sprt1-x^2

Integral of (arcsin^2x)/sprt1-x^2 dx

The solution

You have entered [src]

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

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

Integral(asin(x)^2/(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:
  
  $\int \frac{\operatorname{asin}^{2}{\left(x \right)}}{\sqrt{1}}\, dx = \int \operatorname{asin}^{2}{\left(x \right)}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $x \operatorname{asin}^{2}{\left(x \right)} - 2 x + 2 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}$
  So, the result is: $x \operatorname{asin}^{2}{\left(x \right)} - 2 x + 2 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}$
The result is: $- \frac{x^{3}}{3} + x \operatorname{asin}^{2}{\left(x \right)} - 2 x + 2 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$$x\,\arcsin ^2x+2\,\sqrt{1-x^2}\,\arcsin x-{{x^3}\over{3}}-2\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

        2
  7   pi 
- - + ---
  3    4

$${{3\,\pi^2-28}\over{12}}$$

        2
  7   pi 
- - + ---
  3    4

$$- \frac{7}{3} + \frac{\pi^{2}}{4}$$

Simplify

Numerical answer [src]

0.134067766939006

0.134067766939006

The graph

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

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Integral of (arcsin^2x)/sprt1-x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution