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;

Question

3)积分号[cos2x/(cosx+sinx)]dx;4)积分号[(x^3-27)/(x-3)]dx
有答案,但不知道过程.请大家帮忙解一下,谢谢!

Answer 1

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+C.

积分号[(x^3-27)/(x-3)]dx
=∫[x^2+3x+9]dx
=x^3/3+3x^2/2+9x+C.