Mister Exam

Integral of arcsin2x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 1/4            
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 |  asin(2*x) dx
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$$\int\limits_{0}^{\frac{1}{4}} \operatorname{asin}{\left(2 x \right)}\, dx$$
Integral(asin(2*x), (x, 0, 1/4))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

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

        1. Use integration by parts:

          Let and let .

          Then .

          To find :

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

          Now evaluate the sub-integral.

        2. Let .

          Then let and substitute :

          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:

          Now substitute back in:

        So, the result is:

      Now substitute back in:

    Method #2

    1. Use integration by parts:

      Let and let .

      Then .

      To find :

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

      Now evaluate the sub-integral.

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

      1. Let .

        Then let and substitute :

        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:

        Now substitute back in:

      So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
                         __________              
  /                     /        2               
 |                    \/  1 - 4*x                
 | asin(2*x) dx = C + ------------- + x*asin(2*x)
 |                          2                    
/                                                
$$\int \operatorname{asin}{\left(2 x \right)}\, dx = C + x \operatorname{asin}{\left(2 x \right)} + \frac{\sqrt{1 - 4 x^{2}}}{2}$$
The graph
The answer [src]
        ___     
  1   \/ 3    pi
- - + ----- + --
  2     4     24
$$- \frac{1}{2} + \frac{\pi}{24} + \frac{\sqrt{3}}{4}$$
=
=
        ___     
  1   \/ 3    pi
- - + ----- + --
  2     4     24
$$- \frac{1}{2} + \frac{\pi}{24} + \frac{\sqrt{3}}{4}$$
-1/2 + sqrt(3)/4 + pi/24
Numerical answer [src]
0.063912395791794
0.063912395791794

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