Can someone help me with these?

Question

dx/(x sqrt(x^3 -1) using x^3 = 1/z^2 i.e z^-2/3

it x(third power)- 1 just to be clear.

dx/(x(a+bx^n)) using x^n = 1/z i.e. x= z^-1/n

Thank You for the help!

Answer 1

Hmmm.

dx/(x√(x^3-1))
as you suggest, let

x^3 = 1/z^2
x = z^(-2/3)
dx = -2/3 z^(-5/3) dz
1/x = z^(2/3)
√(x^3-1) = √(1/z^2 - 1) = √(1-z^2)/z
so now you have an integrand of

-2/3 z^(-5/3) dz z^(2/3) z
-------------------------------
√(1-z^2)

= -2/3 dz/√(1-z^2)

Hmmm. This does not agree with the result at wolframalpha, so better double-check my math.