oo / | | /1\ | asin|-| dx | \x/ | / 2
Integral(asin(1/x), (x, 2, oo))
Use integration by parts:
Let and let .
Then .
To find :
The integral of a constant is the constant times the variable of integration:
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:
Don't know the steps in finding this integral.
But the integral is
So, the result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | // | 2| \ | /1\ /1\ || acosh(x) for |x | > 1| | asin|-| dx = C + x*asin|-| + |< | | \x/ \x/ ||-I*asin(x) otherwise | | \\ / /
oo - acosh(2)
=
oo - acosh(2)
oo - acosh(2)
Use the examples entering the upper and lower limits of integration.