∫(x+2)/(4x-x^2)^1/2dx
问题描述:
∫(x+2)/(4x-x^2)^1/2dx
答
∫[x/√(3+4x+x^2)]dx =∫{x/√[(x^2+4x+4)-1]}dx =∫{x/√[(x+2)^2-1]}dx =∫{[(x+2)-2]/√[(x+2)^2-1]}d(x+2). 令x+2=1/sinu,则:d(x+2)=[cosu/(sinu)^2]du, ∴∫[x/√(3+4x+x^2)]dx =∫..