用换元法求∫(2,1)(根号x^2-1)/x dx

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用换元法求∫(2,1)(根号x^2-1)/x dx
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用换元法求∫(2,1)(根号x^2-1)/x dx
用换元法求∫(2,1)(根号x^2-1)/x dx

用换元法求∫(2,1)(根号x^2-1)/x dx

令x=sect,则dx=sect·tant dt
∫(1→2)√(x²-1)/xdx
=∫(0→π/3)tan²t dt
=∫(0→π/3)(sec²t-1)dt
=(tant-t)|(0→π/3)
=tanπ/3-π/3
=√3-π/3