求下列积分 1.∫(x+2倍根号x+3)/x dx 2.∫(x^2+sin^2x)/x^2sin^2x dx 3.∫cos^2(x/2) dx 谢啦,

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求下列积分 1.∫(x+2倍根号x+3)/x dx 2.∫(x^2+sin^2x)/x^2sin^2x dx 3.∫cos^2(x/2) dx 谢啦,
求下列积分 1.∫(x+2倍根号x+3)/x dx 2.∫(x^2+sin^2x)/x^2sin^2x dx 3.∫cos^2(x/2) dx 谢啦,

求下列积分 1.∫(x+2倍根号x+3)/x dx 2.∫(x^2+sin^2x)/x^2sin^2x dx 3.∫cos^2(x/2) dx 谢啦,
1
∫(x+2√x+3)dx/x =∫dx+∫2dx/√x+∫3dx/x
=x+4√x+3lnx+C
2
∫(x^2+(sinx)^2)dx/[x^2(sinx)^2]
=∫dx/(sinx)^2+∫dx/x^2
=-cotx+(-1/x)+C
(cotx)'=-sinx/sinx-cosx^2/(sinx)^2=-(1+(cotx)^2)=-1/(sinx)^2
3
∫(cos(x/2))^2dx
=∫(1+cosx)dx/2
=x/2+sinx/2+C