求解根号下(5-4x-x^2)的不定积分
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求解根号下(5-4x-x^2)的不定积分
希望重要过程详细点.谢谢
希望重要过程详细点.谢谢
![求解根号下(5-4x-x^2)的不定积分](/uploads/image/z/8606483-35-3.jpg?t=%E6%B1%82%E8%A7%A3%E6%A0%B9%E5%8F%B7%E4%B8%8B%EF%BC%885-4x-x%5E2%EF%BC%89%E7%9A%84%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86)
∫√(5-4x-x^2)dx
=∫√[9-(x+2)^2]dx
x+2=3sinu dx=d(x+2)=d3sinu=3cosudu
=∫9cosu^2du
=(9/2)∫(1+cos2u)du
=(9/2)u+(9/4)sin2u+C
=(9/2)u+(9/2)sinucosu+C
=(9/2)arcsin[(x+2)/3] +(9/2)[(x+2)/3]√(1-(x+2)^2/9) +C
=(9/2)arcsin[(x+2)/3] +(1/2)(x+2)√(5-4x-x^2) +C
=∫√[9-(x+2)^2]dx
x+2=3sinu dx=d(x+2)=d3sinu=3cosudu
=∫9cosu^2du
=(9/2)∫(1+cos2u)du
=(9/2)u+(9/4)sin2u+C
=(9/2)u+(9/2)sinucosu+C
=(9/2)arcsin[(x+2)/3] +(9/2)[(x+2)/3]√(1-(x+2)^2/9) +C
=(9/2)arcsin[(x+2)/3] +(1/2)(x+2)√(5-4x-x^2) +C