求不定积分 1/x^2·根号下x^2+4 x/sinx^2这是两个。第一个是 1/x^2·根号下x^2+4第二个是 x/sinx^2
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∫ √(x^2+4)/x^2 dx
letx=2tany
dx = 2(secy)^2 dy
∫ √(x^2+4)/x^2 dx
=(1/2)∫ [secy/(tany)^2] dy
=(1/2)∫ [cosy/(siny)^2] dy
= -(1/2)(1/siny) + C
=-(1/2)[√(x^2+4) /x] + C
∫ x/sin(x^2) dx
=(1/2)∫ csc(x^2) dx^2
=(1/2)ln|csc(x^2)-cot(x^2)| + C