Question

∫dx/(x√(4-x²))？

Answer 1

本题的思路是换元法，设x=2sint，则：
4-x^2
=4-4sin^2t
=4cos^2t.
dx=d2sint=2costdt.

Answer 2

x=2sinu
dx=2cosu du
∫dx/[x√(4-x^2)]
=∫2cosu du/[4sinu.cosu]
=(1/2)∫ cscu du
=(1/2)ln|cscu -cotu | + C
=(1/2)ln| 2/x - √(4-x^2)/x | + C