∫dx/（x^2—2x+5)^(1/2)
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∫ dx/√(x²-2x+5)
= ∫ dx/[(x-1)²+4]
x-1 = 2tant，dx = 2sec²t dt，sect = (1/2)√[(x-1)²+4] = (1/2)√(x²-2x+5)
原式= ∫ 2sec²t/√(4tan²t+4) dt
= ∫ 2sec²t/(2sect) dt
= ∫ sect dt
= ∫ sect * (sect+tant)/(sect+tant) dt
= ∫ (sect*tant+sec²t)/(sect+tant) dt
= ∫ d(sect+tant)/(sect+tant) dt
= ln|sect+tant| + C
= ln|(x-1)/2 + (1/2)√(x²-2x+5)| + C
= ln|x-1+√(x²-2x+5)| + C'
= ∫ dx/[(x-1)²+4]
x-1 = 2tant，dx = 2sec²t dt，sect = (1/2)√[(x-1)²+4] = (1/2)√(x²-2x+5)
原式= ∫ 2sec²t/√(4tan²t+4) dt
= ∫ 2sec²t/(2sect) dt
= ∫ sect dt
= ∫ sect * (sect+tant)/(sect+tant) dt
= ∫ (sect*tant+sec²t)/(sect+tant) dt
= ∫ d(sect+tant)/(sect+tant) dt
= ln|sect+tant| + C
= ln|(x-1)/2 + (1/2)√(x²-2x+5)| + C
= ln|x-1+√(x²-2x+5)| + C'
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