作者Eliphalet (信我，会很劲的)
站内trans_math
标题Re: [积分] 三角函数积分
时间Wed Jan 14 13:17:17 2009
※ 引述《icola (Br)》之铭言：
: ∫1/(1+sinx)dx=?
: 请版上大大告诉我详解好吗?
: 谢谢
: ans : tanx-secx+C
1 + sin(x) = 2 sin(π/4 + x/2 ) cos(π/4 - x/2 )
= 2 sin ( (π/2) - (π/4 - x/2) ) cos(π/4 - x/2 )
= 2 ( cos(π/4 - x/2 ) )^2
=> ∫1/(1+sinx)dx = - tan(π/4 - x/2) + C
- cos(x)
= ---------------- + C
1 + sin(x)
= tan(x) - sec(x) + C
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