Mister Exam

Other calculators

Integral of x*asin(x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1              
  /              
 |               
 |        / 2\   
 |  x*asin\x / dx
 |               
/                
0                
$$\int\limits_{0}^{1} x \operatorname{asin}{\left(x^{2} \right)}\, dx$$
Integral(x*asin(x^2), (x, 0, 1))
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 is when :

      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:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                       ________              
 |                       /      4     2     / 2\
 |       / 2\          \/  1 - x     x *asin\x /
 | x*asin\x / dx = C + ----------- + -----------
 |                          2             2     
/                                               
$$\int x \operatorname{asin}{\left(x^{2} \right)}\, dx = C + \frac{x^{2} \operatorname{asin}{\left(x^{2} \right)}}{2} + \frac{\sqrt{1 - x^{4}}}{2}$$
The graph
The answer [src]
  1   pi
- - + --
  2   4 
$$- \frac{1}{2} + \frac{\pi}{4}$$
=
=
  1   pi
- - + --
  2   4 
$$- \frac{1}{2} + \frac{\pi}{4}$$
-1/2 + pi/4
Numerical answer [src]
0.285398163397448
0.285398163397448

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