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Identical expressions
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Similar expressions
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Solving integrals/ 3*arcsin^3(x)/sqrt(1-x^2)

Integral of 3*arcsin^3(x)/sqrt(1-x^2) dx

The solution

You have entered [src]

  1               
  /               
 |                
 |         3      
 |   3*asin (x)   
 |  ----------- dx
 |     ________   
 |    /      2    
 |  \/  1 - x     
 |                
/                 
0

$$\int\limits_{0}^{1} \frac{3 \operatorname{asin}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}}\, dx$$

Integral(3*asin(x)^3/(sqrt(1 - x^2)), (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{3 \operatorname{asin}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}}\, dx = 3 \int \frac{\operatorname{asin}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}}\, dx$
1. Let $u = \operatorname{asin}{\left(x \right)}$ .
  
  Then let $du = \frac{dx}{\sqrt{1 - x^{2}}}$ and substitute $du$ :
  
  $\int u^{3}\, du$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int u^{3}\, du = \frac{u^{4}}{4}$
  Now substitute $u$ back in:
  
  $\frac{\operatorname{asin}^{4}{\left(x \right)}}{4}$
So, the result is: $\frac{3 \operatorname{asin}^{4}{\left(x \right)}}{4}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$${{3\,\arcsin ^4x}\over{4}}$$

Simplify

The answer [src]

    4
3*pi 
-----
  64

$${{3\,\pi^4}\over{64}}$$

    4
3*pi 
-----
  64

$$\frac{3 \pi^{4}}{64}$$

Упростить

Numerical answer [src]

4.56605113785735

4.56605113785735

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

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Integral of 3*arcsin^3(x)/sqrt(1-x^2) dx

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The solution