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Identical expressions
asin(three *x)/sqrt(one - nine *x^ two)
arc sinus of e of (3 multiply by x) divide by square root of (1 minus 9 multiply by x squared )
arc sinus of e of (three multiply by x) divide by square root of (one minus nine multiply by x to the power of two)
asin(3*x)/√(1-9*x^2)
asin(3*x)/sqrt(1-9*x2)
asin3*x/sqrt1-9*x2
asin(3*x)/sqrt(1-9*x²)
asin(3*x)/sqrt(1-9*x to the power of 2)
asin(3x)/sqrt(1-9x^2)
asin(3x)/sqrt(1-9x2)
asin3x/sqrt1-9x2
asin3x/sqrt1-9x^2
asin(3*x) divide by sqrt(1-9*x^2)
asin(3*x)/sqrt(1-9*x^2)dx
Similar expressions
asin(3*x)/sqrt(1+9*x^2)
arcsin(3*x)/sqrt(1-9*x^2)

Solving integrals/ asin(3*x)/sqrt(1-9*x^2)

Integral of asin(3x)/sqrt(1-9x^2) dx

The solution

You have entered [src]

 1/6                
  /                 
 |                  
 |    asin(3*x)     
 |  ------------- dx
 |     __________   
 |    /        2    
 |  \/  1 - 9*x     
 |                  
/                   
0

$$\int\limits_{0}^{\frac{1}{6}} \frac{\operatorname{asin}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}}\, dx$$

Integral(asin(3*x)/sqrt(1 - 9*x^2), (x, 0, 1/6))

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = \operatorname{asin}{\left(3 x \right)}$ .
  
  Then let $du = \frac{3 dx}{\sqrt{1 - 9 x^{2}}}$ and substitute $\frac{du}{3}$ :
  
  $\int \frac{u}{3}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int u\, du = \frac{\int u\, du}{3}$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u\, du = \frac{u^{2}}{2}$
    So, the result is: $\frac{u^{2}}{6}$
  Now substitute $u$ back in:
  
  $\frac{\operatorname{asin}^{2}{\left(3 x \right)}}{6}$
Method #2
1. Let $u = 3 x$ .
  
  Then let $du = 3 dx$ and substitute $\frac{du}{3}$ :
  
  $\int \frac{\operatorname{asin}{\left(u \right)}}{3 \sqrt{1 - u^{2}}}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{\operatorname{asin}{\left(u \right)}}{\sqrt{1 - u^{2}}}\, du = \frac{\int \frac{\operatorname{asin}{\left(u \right)}}{\sqrt{1 - u^{2}}}\, du}{3}$
    1. Let $u = \operatorname{asin}{\left(u \right)}$ .
      
      Then let $du = \frac{du}{\sqrt{1 - u^{2}}}$ and substitute $du$ :
      
      $\int u\, du$
      
      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:
      
      $\frac{\operatorname{asin}^{2}{\left(u \right)}}{2}$
    So, the result is: $\frac{\operatorname{asin}^{2}{\left(u \right)}}{6}$
  Now substitute $u$ back in:
  
  $\frac{\operatorname{asin}^{2}{\left(3 x \right)}}{6}$
Add the constant of integration:

$\frac{\operatorname{asin}^{2}{\left(3 x \right)}}{6}+ \mathrm{constant}$

The answer is:

$\frac{\operatorname{asin}^{2}{\left(3 x \right)}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                 
 |                            2     
 |   asin(3*x)            asin (3*x)
 | ------------- dx = C + ----------
 |    __________              6     
 |   /        2                     
 | \/  1 - 9*x                      
 |                                  
/

$$\int \frac{\operatorname{asin}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}}\, dx = C + \frac{\operatorname{asin}^{2}{\left(3 x \right)}}{6}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  2
pi 
---
216

$$\frac{\pi^{2}}{216}$$

  2
pi 
---
216

$$\frac{\pi^{2}}{216}$$

pi^2/216

Numerical answer [src]

0.0456926129680063

0.0456926129680063

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

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Identical expressions

Similar expressions

Integral of asin(3x)/sqrt(1-9x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of asin(3*x)/sqrt(1-9*x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2

Integral of asin(3x)/sqrt(1-9x^2) dx