作者kk813140 (7413520)
看板trans_math
标题Re: [积分] ∫(secX)^3 dx ...
时间Thu Mar 11 03:33:44 2010
整理一下..
※ 引述《andy2007 (痴汉堡王)》之铭言：
Let u = secX dv = secX^2 dx
du = secXtanX v = tanX
∫udv = uv - ∫vdu
∫secX^3 dx = secX * secX^2 dx
= secXtanX - ∫tanX * secXtanX dx
= secXtanX - ∫secXtanX^2 dx
= secXtanX - ∫secX^3 - secX dx (因为tanX^2 = secX^2 - 1)
= secXtanX - ∫secX^3 +∫secX dx
将右式中的∫secX^3 移向
=> 2∫secX^3 dx = secXtanX +∫secX dx
∫secX^3 dx = ( secXtanX + ln|secx+tanx| )/2 + c
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