This document contains mathematical integrals expressed in LaTeX format. It shows the setup and solving of four integrals: the integral of 1/(1-x^2), the integral of x^2*x^(i-1), the integral of x^4/x^5-3, and the integral of (x^(i-1))^(1/2). Each integral is set up, the substitution or technique used to solve it is identified, and the final solution with the +C term is provided.

1. ∫xdx/(1-x²)=
-½∫(1-x²)-²(-2)xdx
V=1-x²
DV=-2xdx ̸ = -½ (1-x²)/1+c
=½(1-x²)¯ⁱ4c

2. ∫x² xⁱ-1dx
⅓∫(xⁱ-1)½ 3x²dx
V=xⁱ-1
DV=3x²dx /= ⅓ (xⁱ-1)ⁱ'² 3/2+c
=2/9=(xⁱ-1)ⁱ’²+c

3. ∫x⁴dx/x⁵-3=
⅕∫(x⁵-3)¯⅟² 5x⁴dx=
⅕(x⁵-3) ⅟² +c =
2/5√x⁵-3+c