Integral leading to the Arcsin:
Reciprocal of radical of a general quadratic: Find
.
This has a negative coefficient of x2, suggesting the integral leading to the Arcsin.
Let's see if completing the square in the quantity under the radical sign helps:
. Substituting this result, we get
![]()
Let
,
,
. Then I becomes
. Now we use the integral leading to the Arcsin to get
. Finally, we express the result in terms of x:
![]()