问：数学 secx不定积分 怎么做啊 从这步怎么推到下一步？求大神解答 请教高数题:secX的不定积分该怎么求啊?
\u4e0d\u5b9a\u79ef\u5206\uff0c\u8fd9\u4e00\u6b65\u5230\u8fd9\u4e00\u6b65\u600e\u4e48\u6765\u7684\uff1f\u8fd9\u4e2a\u5176\u5b9e\u7b97\u662f\u5e38\u7528\u79ef\u5206\u516c\u5f0f\u4e86\uff0c\u4e0d\u8fc7\u4e0d\u77e5\u9053\u7684\u8bdd\u53ef\u4ee5\u6362\u5143\u63a8\u5bfc\uff1a
\u4ee5\u4e0a\uff0c\u8bf7\u91c7\u7eb3\u3002\u222bsecx dx\u7684\u79ef\u5206\u516c\u5f0f\u603b\u8bb0\u5f97\u7684\u5427\uff1f
=ln|tanx+secx|+c
\u4e0d\u59a8\u5148\u6c42 CSCx \u4e0d\u5b9a\u79ef\u5206
=dx/sinx=dx/2sinx/2cosx/2=d(x/2)/(tanx/2*cos^2(x/2))=d(tanx/2)/tanx/2=ln|tanx/2|+c
=ln|cscx-cotx|+c
\u6c42 secx \u4e0d\u5b9a\u79ef\u5206 \u5c31\u662fcsc(x+\u03c0/2)d(x+\u03c0/2)
=ln|secx+tanx|+c
=∫d(sinx)/[(1-sinx)(1+sinx)]
=∫d(sinx) * [1/(1-sinx) + 1/(1+sinx)] * (1/2)
=(1/2)*[∫d(sinx)/(1-sinx) + ∫d(sinx)/(1+sinx)]
=1/2*[-∫d(1-sinx)/(1-sinx) + ∫d(1+sinx)/(1+sinx)]
=1/2*[-ln|1-sinx| + ln|1+sinx|] + C
=1/2*ln|(1+sinx)/(1-sinx)| + C
=1/2*ln|(1+sinx)²/(1-sin²x)| + C 注：分子、分母同乘以 (1+sinx)
=1/2*ln|(1+sinx)²/cos²x| + C
=1/2*ln|(1+sinx)/cosx|² + C
=1/2 * 2 * ln|(1+sinx)/cosx| + C
=ln|(1/cosx + sinx/cosx)| + C
=ln|secx + tanx| + C
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