高等数学微积分,微积分

令 x=(sint)^2,则 dx=2sintcostdt
I=∫[√(1-x)/(1-√x)]dx=2∫[cost/(1-sint)]sintcostdt
=2∫[sint(cost)^2/(1-sint)]dt=2∫sint(1+sint)dt
=2∫[sint+(sint)^2]dt=∫[2sint+1-cos(2t)]dt
=[t-2cost-sin(2t)/2]=2+π/6-5√3/4.