求定积分，有步骤谢谢 30
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思路：
令x=tant
dx=sec²tdt
x=1,t=π/4
x=√3，t=π/3
所以
原式=∫(π/4,π/3)sec²t/[tan²t ·sect] dt
=∫(π/4,π/3)sect/[tan²t ] dt
=∫(π/4,π/3)(1/cost)/[(sint/cost)² ] dt
=∫(π/4,π/3)cost/sin²t dt
=∫(π/4,π/3)1/sin²t dsint
=-1/sint |(π/4,π/3)
=-1/(√3/2)+1/(√2/2)
=-2√3/3 +√2
令x=tant
dx=sec²tdt
x=1,t=π/4
x=√3，t=π/3
所以
原式=∫(π/4,π/3)sec²t/[tan²t ·sect] dt
=∫(π/4,π/3)sect/[tan²t ] dt
=∫(π/4,π/3)(1/cost)/[(sint/cost)² ] dt
=∫(π/4,π/3)cost/sin²t dt
=∫(π/4,π/3)1/sin²t dsint
=-1/sint |(π/4,π/3)
=-1/(√3/2)+1/(√2/2)
=-2√3/3 +√2
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