Re: [積分] 一題積分

[RAINDD (標籤貼爽了沒？)]

※ 引述《pobm (待從頭收拾舊河山)》之銘言：
:          dx
: ∫ --------------
:      1+(cosx)^2

          (sec(x))^2                     1
=  ∫ ----------------- dx  =  ∫ ----------------- d(tan(x))
        1 + (sec(x))^2              2 + (tan(x))^2

           1                                              1/√2
=  ∫ ----------- dt {令 t = tan(x) }  =  (1/√2)∫ ---------------- dt
        2 + t^2                                       1 + (t/√2)^2

=  (1/√2) arctan(t/√2) + constant

=  arctan(tan(x)/√2) / √2 + constant

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 61.64.93.146
推 pobm:謝謝^^