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x*asin(x)

Integral of x*asin(x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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

    Let and let .

    Then .

    To find :

    1. The integral of is when :

    Now evaluate the sub-integral.

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

      SqrtQuadraticDenomRule(a=1, b=0, c=-1, coeffs=[1, 0, 0], context=x**2/sqrt(1 - x**2), symbol=x)

    So, the result is:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
                                                  ________
  /                              2               /      2 
 |                    asin(x)   x *asin(x)   x*\/  1 - x  
 | x*asin(x) dx = C - ------- + ---------- + -------------
 |                       4          2              4      
/                                                         
$$\int x \operatorname{asin}{\left(x \right)}\, dx = C + \frac{x^{2} \operatorname{asin}{\left(x \right)}}{2} + \frac{x \sqrt{1 - x^{2}}}{4} - \frac{\operatorname{asin}{\left(x \right)}}{4}$$
The graph
The answer [src]
pi
--
8 
$$\frac{\pi}{8}$$
=
=
pi
--
8 
$$\frac{\pi}{8}$$
Numerical answer [src]
0.392699081698724
0.392699081698724
The graph
Integral of x*asin(x) dx

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