求下列不定积分:)积分号[(x^2+根号下x^3+3x)/根号下x]dx;2)积分号[sin(x/2)]^2dx;

题目

求下列不定积分:)积分号[(x^2+根号下x^3+3x)/根号下x]dx;2)积分号[sin(x/2)]^2dx;
3)积分号[cos2x/(cosx+sinx)]dx;4)积分号[(x^3-27)/(x-3)]dx

答案

积分号[(x^2+根号下x^3+3x)/根号下x]dx=∫[x^(3/2)+x+3x^(1/2)]dx=(2/5)x^(5/2)+x^2/2+2x^(3/2)+C.积分号[sin(x/2)]^2dx=∫[1/2-(cosx)/2]dx=x/2-(sinx)/2+C积分号[cos2x/(cosx+sinx)]dx=∫[cosx-sinx]dx=sinx+cosx+...