indefinite integration

1a. Show that 1-cosx/(1+cosx) = tan^2(x/2)

b. Given that ∫(1-cosx)/(1+cosx) dx = 2tan(x/2) -x +C
Find ∫ cosx/(1+cosx) dx

2. Given that ∫ tan^2xsecx dx = 1/2 tanxsecx-1/2 ln (secx+tanx) +C
Find ∫ tan^2(x/2)sec^3(x/2) dx

3. Given that ∫ dx/(x^2-9) =1/6 ln (x-3/x+3) +C
Find ∫ 2x+3 / ((x-6)(x+3)^(1/2) dx

4. Given that ∫ sec^3x dx = 1/2 secxtanx +1/2 ln(secx+tanx) + C
Find ∫ (1+x^2)^(1/2) -(x^2-1)^(1/2) dx