数学题目。
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令 x = sect, 则 dx = sect tant dt, cost = 1/x, t = arccos(1/x),
I = ∫sect tant dt / [(sect)^3 tant] = ∫ dt / (sect)^2 = ∫ (cost)^2 dt
= (1/2)∫ (1+cos2t) dt = (1/2)t + (1/4)sin2t = (1/2)t + (1/2)sintcost
=(1/2)arccos(1/x) + √(x^2-1)/(2x^2) + C
I = ∫sect tant dt / [(sect)^3 tant] = ∫ dt / (sect)^2 = ∫ (cost)^2 dt
= (1/2)∫ (1+cos2t) dt = (1/2)t + (1/4)sin2t = (1/2)t + (1/2)sintcost
=(1/2)arccos(1/x) + √(x^2-1)/(2x^2) + C
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