∫cosx/根号下sinxdx、∫x^2/(a^2+x^3)^1/2、∫xdx/x^2+3、∫e^1/x/x^2dx、∫

∫ cosx/√sinx dx
=∫ 1/√sinx d(sinx)
=2√sinx+C
∫x²/(a²+x²)^1/2 dx
=(1/3)∫1/(a²+x²)^1/2 d(x³)
=(2/3)(a²+x²)^1/2+C
∫x/(x²+3) dx
=(1/2)∫ 1/(x²+3) dx
=(1/2)ln(x²+3)+C
∫e^(1/x) /x² dx
=-∫e^(1/x) d(1/x)
=-e^(1/x)+C
∫e^(-2x)dx
=-(1/2)∫e^(-2x)d(-2x)
=-(1/2)e^(-2x)+C