plush dirge
I understand u-sub and integration by parts and how to do it. What I dont understand is how you intuitively know what method to use. In this problem, I think you could use LIPET to decide what u and dv are to do by parts, but how do I know if I can do it using a more simple method like standard u-sub? Since nothing in the denominator of the integrand can give me archsin(x), should I just default to by parts?
lunar islandBOT
wintry bluff
When you have roots of type $\sqrt{ax^2+b}$, trigonometric substitution is almost always going to be the answer. Like in this example.
mortal steepleBOT
0x
wintry bluff
Integration by parts won't help you here as you won't be able to integrate $(1-x^2)^{-\frac{1}{2}}$ without substitution.
mortal steepleBOT
0x
wintry bluff
That being said, are you able to evaluate this integral?