求不定积分 1/x^2·根号下x^2+4 x/sinx^2
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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
这是两个。第一个是 1/x^2·根号下x^2+4
第二个是 x/sinx^2
![求不定积分 1/x^2·根号下x^2+4 x/sinx^2](/uploads/image/z/4422752-8-2.jpg?t=%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86+1%2Fx%5E2%C2%B7%E6%A0%B9%E5%8F%B7%E4%B8%8Bx%5E2%2B4+x%2Fsinx%5E2)
∫ √(x^2+4)/x^2 dx
let
x=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
let
x=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