∫x的平方/根号下4-9x的平方 ·dx
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令x=(2/3)sint 则sint=3x/2cost=根号(1-sin^2t)=根号(1-9x^2/4)=2分之根号(4-9x^2)dx=(2/3)costdt∫x^2/根号(4-9x^2)*dx=∫(4/9)sin^2t/2cost (2/3)costdt=2/27∫(1-cos2t)dt=2/27(t-sintcost)+C=2/27[arcsin(3/2)x-4分之3x*根号(4-9x^2)]+C
咨询记录 · 回答于2023-02-15
∫x的平方/根号下4-9x的平方 ·dx
令兄告册羡宏x=(2/3)sintdx=(2/3)costdt∫友悉x^2/根号(4-9x^2)*dx=∫(4/9)sin^2t/2cost (2/3)costdt=2/27∫(1-cos^2t)dt
令x=(2/3)sintdx=(2/3)costdt∫x^2/根棚好颂号袜圆(4-9x^2)*dx=∫(4/9)sin^2t/2cost (2/3)costdt=2/27∫链郑(1-cos2t)dt
令x=(2/3)sintdx=(2/3)costdt∫x^2/根肆则哗号盯磨(4-9x^2)*dx=∫(4/9)sin^2t/2cost (2/3)costdt=2/27∫(1-cos2t)dt=2/27(t-sintcost)+C=2/27[arcsin3x/2-3x/4 根裂行号(4-9x)]+C
令x=(2/3)sint 则sint=3x/2cost=根号(1-sin^2t)=根号(1-9x^2/4)=2分之如衡根枝银号(4-9x^2)dx=(2/3)costdt∫x^2/根号猛橡宴(4-9x^2)*dx=∫(4/9)sin^2t/2cost (2/3)costdt=2/27∫(1-cos2t)dt=2/27(t-sintcost)+C=2/27[arcsin3x/2-3x/4 根号(4-9x)]+C
令x=(2/3)sint 则纤答游sint=3x/2cost=根号(1-sin^2t)=根号(1-9x^2/4)=2分之根号毁销(4-9x^2)dx=(2/3)costdt∫x^2/根号举前(4-9x^2)*dx=∫(4/9)sin^2t/2cost (2/3)costdt=2/27∫(1-cos2t)dt=2/27(t-sintcost)+C=2/27[arcsin(3/2)x-4分之3x*根号(4-9x^2)]+C
最后一段是正确答案
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