①∫（1-x）/√9-4x² dx

题目

①∫（1-x）/√9-4x² dx
②∫√x²-9/x dx
③∫dx/√1+e^x

答案

①(1-x)/(9-4x^2)^(12)=12(94-x^2)^(12)
-4x/4(9-4x^2)^(12)
∴∫（1-x）/√9-4x² dx
=(1/2)*arcsin(2x/3)+(1/4)*(9-4x^2)^(1/2)+C
②设x=3sect 0