根号下(1-x^2)dx/x^2的不定积分 dx/根号下1-x^2的不定积分 请用第二次换元法求,
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根号下(1-x^2)dx/x^2的不定积分 dx/根号下1-x^2的不定积分 请用第二次换元法求,
![根号下(1-x^2)dx/x^2的不定积分 dx/根号下1-x^2的不定积分 请用第二次换元法求,](/uploads/image/z/3909883-67-3.jpg?t=%E6%A0%B9%E5%8F%B7%E4%B8%8B%EF%BC%881-x%5E2%EF%BC%89dx%2Fx%5E2%E7%9A%84%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86+dx%2F%E6%A0%B9%E5%8F%B7%E4%B8%8B1-x%5E2%E7%9A%84%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86+%E8%AF%B7%E7%94%A8%E7%AC%AC%E4%BA%8C%E6%AC%A1%E6%8D%A2%E5%85%83%E6%B3%95%E6%B1%82%2C)
∫ (√(1-x^2) /x^2) dx
let
x= siny
dx= cosy dy
∫ (√(1-x^2) /x^2) dx
= ∫ (coty)^2 dy
= ∫ [(cscy)^2 - 1] dy
= -coty - y + C
= - √(1-x^2) /x - arcsinx + C
∫ (1/√(1-x^2)) dx
let
x = siny
dx = cosy dy
∫ (1/√(1-x^2)) dx
=∫ dy
=y + C
= arcsinx + C
let
x= siny
dx= cosy dy
∫ (√(1-x^2) /x^2) dx
= ∫ (coty)^2 dy
= ∫ [(cscy)^2 - 1] dy
= -coty - y + C
= - √(1-x^2) /x - arcsinx + C
∫ (1/√(1-x^2)) dx
let
x = siny
dx = cosy dy
∫ (1/√(1-x^2)) dx
=∫ dy
=y + C
= arcsinx + C