1.∫sec^3/2xtanxdx= 2.∫sin2xdx/根号(1+cos^2x)=

∫ (secx)^(3/2) • tanx dx
= ∫ (secx)^(1 + 1/2) • tanx dx
= ∫ √(secx) • secxtanx dx
= ∫ √(secx) d(secx)
= (2/3)(secx)^(3/2) + C
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∫ (sin2x)/√(1 + cos²x) dx = ∫ (2sinxcosx)/√(1 + cos²x) dx
(v = cos²x,dv = (2cosx)(- sinx) dx)
= ∫ - 1/√(1 + v) dv
= - ∫ (1 + v)^(- ½) d(1 + v)
= - [(1 + v)^(- ½ + 1)]/(- ½ + 1) + C
= - 2√(1 + v) + C
= - 2√(1 + cos²x) + C