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Identical expressions
(arccos(x)^ five)/(sqrt(one -x^ two))
(arc co sinus of e of (x) to the power of 5) divide by ( square root of (1 minus x squared ))
(arc co sinus of e of (x) to the power of five) divide by ( square root of (one minus x to the power of two))
(arccos(x)^5)/(√(1-x^2))
(arccos(x)5)/(sqrt(1-x2))
arccosx5/sqrt1-x2
(arccos(x)⁵)/(sqrt(1-x²))
(arccos(x) to the power of 5)/(sqrt(1-x to the power of 2))
arccosx^5/sqrt1-x^2
(arccos(x)^5) divide by (sqrt(1-x^2))
(arccos(x)^5)/(sqrt(1-x^2))dx
Similar expressions
(arccos(x)^5)/(sqrt(1+x^2))
(arccosx^5)/(sqrt(1-x^2))

Solving integrals/ (arccos(x)^5)/(sqrt(1-x^2))

Integral of (arccos(x)^5)/(sqrt(1-x^2)) dx

The solution

You have entered [src]

  1               
  /               
 |                
 |        5       
 |    acos (x)    
 |  ----------- dx
 |     ________   
 |    /      2    
 |  \/  1 - x     
 |                
/                 
0

$$\int\limits_{0}^{1} \frac{\operatorname{acos}^{5}{\left(x \right)}}{\sqrt{- x^{2} + 1}}\, dx$$

Integral(acos(x)^5/(sqrt(1 - x^2)), (x, 0, 1))

Detail solution

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

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

$\int u^{5}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- u^{5}\right)\, du = - \int u^{5}\, du$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int u^{5}\, du = \frac{u^{6}}{6}$
  So, the result is: $- \frac{u^{6}}{6}$
Now substitute $u$ back in:

$- \frac{\operatorname{acos}^{6}{\left(x \right)}}{6}$
Add the constant of integration:

$- \frac{\operatorname{acos}^{6}{\left(x \right)}}{6}+ \mathrm{constant}$

The answer is:

$- \frac{\operatorname{acos}^{6}{\left(x \right)}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                              
 |       5                  6   
 |   acos (x)           acos (x)
 | ----------- dx = C - --------
 |    ________             6    
 |   /      2                   
 | \/  1 - x                    
 |                              
/

$$-{{\arccos ^6x}\over{6}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  6
pi 
---
384

$${{\pi^6}\over{384}}$$

  6
pi 
---
384

$$\frac{\pi^{6}}{384}$$

Упростить

Numerical answer [src]

2.50361769160236

2.50361769160236

The graph

Integral of (arccos(x)^5)/(sqrt(1-x^2)) dx

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

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Identical expressions

Similar expressions

Integral of (arccos(x)^5)/(sqrt(1-x^2)) dx

Limits of integration:

The graph:

Piecewise:

The solution