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Integral of arcsin(1/x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 oo           
  /           
 |            
 |      /1\   
 |  asin|-| dx
 |      \x/   
 |            
/             
2             
$$\int\limits_{2}^{\infty} \operatorname{asin}{\left(\frac{1}{x} \right)}\, dx$$
Integral(asin(1/x), (x, 2, oo))
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. The integral of a constant times a function is the constant times the integral of the function:

    1. Don't know the steps in finding this integral.

      But the integral is

    So, the result is:

  3. Now simplify:

  4. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                        
 |                              //                | 2|    \
 |     /1\                /1\   || acosh(x)   for |x | > 1|
 | asin|-| dx = C + x*asin|-| + |<                        |
 |     \x/                \x/   ||-I*asin(x)   otherwise  |
 |                              \\                        /
/                                                          
$$\int \operatorname{asin}{\left(\frac{1}{x} \right)}\, dx = C + x \operatorname{asin}{\left(\frac{1}{x} \right)} + \begin{cases} \operatorname{acosh}{\left(x \right)} & \text{for}\: \left|{x^{2}}\right| > 1 \\- i \operatorname{asin}{\left(x \right)} & \text{otherwise} \end{cases}$$
The graph
The answer [src]
oo - acosh(2)
$$- \operatorname{acosh}{\left(2 \right)} + \infty$$
=
=
oo - acosh(2)
$$- \operatorname{acosh}{\left(2 \right)} + \infty$$
oo - acosh(2)

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