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

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1             
  /             
 |              
 |          2   
 |  /     2\    
 |  \1 - x /    
 |  --------- dx
 |      t       
 |              
/               
0               
$$\int\limits_{0}^{1} \frac{\left(1 - x^{2}\right)^{2}}{t}\, dx$$
Integral((1 - x^2)^2/t, (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. The integral of is when :

      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:

      1. The integral of a constant is the constant times the variable of integration:

      The result is:

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                
 |                           3    5
 |         2              2*x    x 
 | /     2\           x - ---- + --
 | \1 - x /                3     5 
 | --------- dx = C + -------------
 |     t                    t      
 |                                 
/                                  
$$\int \frac{\left(1 - x^{2}\right)^{2}}{t}\, dx = C + \frac{\frac{x^{5}}{5} - \frac{2 x^{3}}{3} + x}{t}$$
The answer [src]
 8  
----
15*t
$$\frac{8}{15 t}$$
=
=
 8  
----
15*t
$$\frac{8}{15 t}$$
8/(15*t)

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