I have a few variations of some problems that would make the entire homework a lot easier. However, our teacher never covered some of these problems, and I would appreciate some assistance?
a. Integral of 1/(x^2(x^2 - 1)^(1/2)) dx
b. Integral of (x^3)/((x^2 + 4)^(1/2)) dx
c. Integral of ((9 - x^2)^(1/2))/x^2 dx
This is all under Trigonometric substitutions, where substitutions include those sec, cos, and tan.
For a., that extra x squared is miffing me. B. the variable in the numerator prevents a convenient substitution. C. x squared in the denominator is unlike anything we were taught in class.