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_数学解答

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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解答

1∫(x+2√x+3)dx/x =∫dx+∫2dx/√x+∫3dx/x=x+4√x+3lnx+C2∫(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)^23∫(cos(x/2))^...