作业帮高等数学不定积分两小题?
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高等数学不定积分两小题?
高等数学不定积分两小题?
高等数学不定积分两小题?
不用下压缩包了东西一样的!
设 x = 2sint，则 dx = 2cost*dt ∫dx/[x*√(4-x^2)] =∫2cost*dt/[2sint*2cost] =∫dt/(2sint) =1/2*∫dt/sint =∫d(t/2)/{2tan(t/2)*[cos(t/2)]^2} =1/2*∫[sec(t/2)]^2*d(t...
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设 x = 2sint，则 dx = 2cost*dt ∫dx/[x*√(4-x^2)] =∫2cost*dt/[2sint*2cost] =∫dt/(2sint) =1/2*∫dt/sint =∫d(t/2)/{2tan(t/2)*[cos(t/2)]^2} =1/2*∫[sec(t/2)]^2*d(t/2)/tan(t/2) =1/2*∫d[tan(t/2)]/tan(t/2) =1/2ln|tan(t/2)| + C =1/2*ln|sin(t/2)/cos(t/2)| + C =1/2*ln|2sin(t/2)cos(t/2)/{2[cos(t/2)]^2}| + C =1/2*ln|sint/(1+cost)| + C =1/2*ln|(x/2)/[1+√(1-x^2/4)]| + C =1/2*ln|x/[2+√(4-x^2)]| + C =1/2*ln|x| -1/2*ln|2+√(4-x^2)| + C
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