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Solving integrals/ arcsin/sqrt(1-x^2)

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

The solution

You have entered [src]

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

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

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

Detail solution

Let $u = \operatorname{asin}{\left(x \right)}$ .

Then let $du = \frac{dx}{\sqrt{1 - x^{2}}}$ and substitute $du$ :

$\int u\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int u\, du = \frac{u^{2}}{2}$
Now substitute $u$ back in:

$\frac{\operatorname{asin}^{2}{\left(x \right)}}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

  2
pi 
---
 8

$$\frac{\pi^{2}}{8}$$

  2
pi 
---
 8

$$\frac{\pi^{2}}{8}$$

pi^2/8

Numerical answer [src]

1.23370054954695

1.23370054954695

The graph

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

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Identical expressions

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

Limits of integration:

The graph:

Piecewise:

The solution