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arcsin(x)*arcsin(x)

Integral of arcsin(x)*arcsin(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                   
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 |  asin(x)*asin(x) dx
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$$\int\limits_{0}^{1} \operatorname{asin}{\left(x \right)} \operatorname{asin}{\left(x \right)}\, dx$$
Integral(asin(x)*asin(x), (x, 0, 1))
Detail solution
  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. Use integration by parts:

    Let and let .

    Then .

    To find :

    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:

    Now evaluate the sub-integral.

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

  4. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                 ________        
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 | asin(x)*asin(x) dx = C - 2*x + x*asin (x) + 2*\/  1 - x  *asin(x)
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$$\int \operatorname{asin}{\left(x \right)} \operatorname{asin}{\left(x \right)}\, dx = C + x \operatorname{asin}^{2}{\left(x \right)} - 2 x + 2 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}$$
The graph
The answer [src]
       2
     pi 
-2 + ---
      4 
$$-2 + \frac{\pi^{2}}{4}$$
=
=
       2
     pi 
-2 + ---
      4 
$$-2 + \frac{\pi^{2}}{4}$$
-2 + pi^2/4
Numerical answer [src]
0.46740110027234
0.46740110027234
The graph
Integral of arcsin(x)*arcsin(x) dx

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