搜搜做题作业网高数求不定积分 总习题四17
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高数求不定积分 总习题四17
往下该怎么算?
往下该怎么算?
如图
下来原式=-(1/2)∫[(u^2)/√(1+u^2)]d(u^2)
=-(1/2)∫{[(1+u^2)-1]/√(1+u^2)}d(u^2)
=-(1/2)∫√(1+u^2)d(1+u^2)+(1/2)∫[1/√(1+u^2)]d(u^2)
=-(1/3)*(1+u^2)^(3/2)+(1/2)arctanu+c
再将u=1/x代入得
-(1/3)*(1+1/x^2)^(3/2)+(1/2)arctan(1/x)+c
=-(1/2)∫{[(1+u^2)-1]/√(1+u^2)}d(u^2)
=-(1/2)∫√(1+u^2)d(1+u^2)+(1/2)∫[1/√(1+u^2)]d(u^2)
=-(1/3)*(1+u^2)^(3/2)+(1/2)arctanu+c
再将u=1/x代入得
-(1/3)*(1+1/x^2)^(3/2)+(1/2)arctan(1/x)+c