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xarcsinx^2
Solving integrals/ xarcsinx^2

Integral of xarcsinx^2 dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1              
  /              
 |               
 |        2      
 |  x*asin (x) dx
 |               
/                
0
$$\int\limits_{0}^{1} x \operatorname{asin}^{2}{\left(x \right)}\, dx$$ 
Integral(x*asin(x)^2, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                       ________        
 |                      2       2       2     2          /      2         
 |       2             x    asin (x)   x *asin (x)   x*\/  1 - x  *asin(x)
 | x*asin (x) dx = C - -- - -------- + ----------- + ---------------------
 |                     4       4            2                  2          
/
$$\int x \operatorname{asin}^{2}{\left(x \right)}\, dx = C + \frac{x^{2} \operatorname{asin}^{2}{\left(x \right)}}{2} - \frac{x^{2}}{4} + \frac{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{2} - \frac{\operatorname{asin}^{2}{\left(x \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
        2
  1   pi 
- - + ---
  4    16
$$- \frac{1}{4} + \frac{\pi^{2}}{16}$$ 
=
= 
        2
  1   pi 
- - + ---
  4    16
$$- \frac{1}{4} + \frac{\pi^{2}}{16}$$ 
-1/4 + pi^2/16
Numerical answer [src] 
0.366850275068085
0.366850275068085
The graph
Integral of xarcsinx^2 dx

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

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