求∫cosx/sin^2xdx; ∫sec5xdx; ∫1/(√x+3√x)dx; ∫[√﹙x-1﹚/x]dx; ∫sin√xdx;

问题描述:

求∫cosx/sin^2xdx; ∫sec5xdx; ∫1/(√x+3√x)dx; ∫[√﹙x-1﹚/x]dx; ∫sin√xdx;

1、∫cosxdx/sin²x=∫cscxcotxdx=-cscx + c2、∫sec5xdx=(1/5)∫sec5xd(5x)=(1/5)ln|sec5x+tan5x| + c3、∫dx/[x^(1/2)+x^(1/3)],u=x^1/6,x=u^6,dx=6u^5du= 6∫u^5du/(u³+u²)= 6∫u³du/(u+1)= 6...