求∫1/[x2√(4+x2)]dx

求∫1/[x²√(4+x²)]dx
【正确答案】：设x=2tan t，则dx=2dt/cos²t，故 ∫={1/[x²√(4+x²)]}dx =∫1/(4tan²t)•[1/(2/cost)]•(2/cos²t)dt =∫(cost/4sin²t)dt=-(1/4sint)+C =-√(4+x²)/(4x)+C(这里已设x﹥0)．