定积分用凑微分法求的话，上下限要变么？感觉和第二换元法一样了 求不定积分的方法有3种，一是第一换元法也叫凑微分法；二是第二...
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\u901a\u5e38\u7684\u89e3\u6cd5\u662f\u6709\u4e09\u79cd\uff0c\u4e0d\u8fc7\u4e0d\u662f\u8fd9\u6837\u5212\u5206\u7684\u3002\u51d1\u5fae\u5206\u7684\u65b9\u6cd5\uff0c\u662f\u4e2d\u56fd\u4eba\u53d1\u660e\u7684
\u8bf4\u6cd5\uff0c\u76ee\u524d\u8fd8\u6ca1\u6709\u4eba\u521b\u9020\u51fa\u4f7f\u6b27\u7f8e\u4eba\u58eb\u63a5\u53d7\u7684\u8bcd\u6c47\u3002\u51d1\u5fae\u5206\u6cd5\u7684\u5b9e\u8d28\uff0c\u5176\u5b9e\u8fd8
\u662f\u4ee3\u6362\u6cd5(Substitution)\uff0c\u800c\u4ee3\u6362\u6cd5\u672c\u8eab\u53c8\u4e94\u82b1\u516b\u95e8\uff0c\u6709\u5f88\u591a\u5f88\u591a\u79cd\uff0c\u4e0d\u4e00\u800c
\u8db3\u3002
\u5206\u90e8\u79ef\u5206\u6cd5(Integration by Parts), \u56fd\u5185\u5916\u4e8b\u4e00\u81f4\u7684\uff0c\u56fd\u5185\u6309\u90e8\u5c31\u73ed\uff0c\u6ca1\u6709
\u53e6\u8f9f\u8e4a\u5f84\u3002
\u7b2c\u4e09\u5e38\u7528\u7684\u65b9\u6cd5\u662f\u6709\u7406\u5206\u5f0f\u79ef\u5206\u6cd5(Integration by Partial Fraction)\uff0c\u56fd\u5185
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\u7b2c\u56db\u79cd\u65b9\u6cd5\u662f\u590d\u6570\u6cd5(complex number)\uff0c\u56fd\u5185\u5728\u8fd9\u65b9\u9762\uff0c\u4e5f\u662f\u7cfb\u7edf\u6027\u5730\u6ca1\u6709\u91cd
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\u5176\u4ed6\u65b9\u6cd5\u8fd8\u6709\u5f88\u591a\uff0c\u8981\u662f\u8bf4\u6e05\u695a\uff0c\u80fd\u5199\u4e0a\u51e0\u672c\u5929\u6570\u3002\u5728\u6b64\u96be\u4ee5\u4e09\u8a00\u4e24\u8bed\u8bf4\u6e05\uff0c
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用换元法，换
绛旓細鐩存帴鍑戝井鍒嗭紝涓嶆崲 鐢ㄦ崲鍏娉曪紝鎹
绛旓細瀹氱Н鍒濡傛灉鐩存帴鐢ㄥ噾寰垎娉曠殑璇濓紝涓婁笅闄涓嶅彉 鈭(0,1)xe^(2x²)dx =(1/4)鈭(0,1)e^(2x²)d2x²=(1/4)e^(2x²)|(0,1)=(1/4)(e^2-1) 鍙橀噺鏄痻 鈭(0,1)xe^(2x²)dx (t=2x²)=(1/4)鈭(0,2)e^(t)dt 鍙橀噺鏄痶 ...
绛旓細涓嶇敤銆備妇涓畝鍗曠殑渚嬪瓙鍚 鑰冭檻杩欎釜绉垎 鐩存帴绠楀緢瀹规槗锛屽鏋滀綘闈炶鍑戝井鍒嗭紝灏辨槸 娉ㄦ剰锛屼綘娌℃湁杩涜鎹㈠厓锛屽彧鏄皢2xdx鍑戞垚浜哾x²锛屾柟渚夸綘杩涜涓瀹氱Н鍒嗭紝涓嶅畾绉垎瀹屾垚鍚庡緱鍒颁竴鏉″叧浜巟鐨勫嚱鏁帮紝浠ｅ叆涓婁笅闄愯绠楀畾绉垎锛屼唬鍏ョ殑鏄痻鐨勫笺傚鏋滀綘浠 閭ｄ箞灏辨湁 浣犺繘琛屼簡鎹㈠厓锛岃繖涓椂鍊欎綘鐨勪笂涓嬮檺瑕佹崲锛屽洜涓...
绛旓細銆愪綘娌℃湁鎹㈠厓锛屽彧鏄垎閮绉垎锛屼笂涓嬮檺鏃犻渶鍙樺寲銆傘
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绛旓細sinxcosx/锛1+cosx鈭2锛塪x=cox/锛1+cosx鈭2锛塪x=璐熺殑0.5*銆1/锛1+cos鈭2锛塪锛1+cos鈭2锛夈戠劧鍚庡氨鐢ㄢ埆1/m dm=銖憁 涓嶈繃姝ゆ椂鐨绉垎涓涓嬬嚎鍙樻垚浜2鍜1,鏈鍚庣粨鏋滄槸0.5銖2,7,鎶妔in鏀惧埌鍚庨潰 灏哻os鐪嬫垚鏂扮殑鍙橀噺璁＄畻 搴旇鏄痩n鐨勫鏁板舰寮,4,
绛旓細鍑戝井鍒涓嶆崲鍏冿紝鏁呬笉蹇呮崲闄愩
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绛旓細sinxcosx/锛1+cosx鈭2锛塪x=cox/锛1+cosx鈭2锛塪x=璐熺殑0.5*銆1/锛1+cos鈭2锛塪锛1+cos鈭2锛夈戠劧鍚庡氨鐢ㄢ埆1/m dm=銖憁 涓嶈繃姝ゆ椂鐨绉垎涓涓嬬嚎鍙樻垚浜2鍜1锛屾渶鍚庣粨鏋滄槸0.5銖2
绛旓細鍑戝井鍒嗘硶锛鏄崲鍏绉垎娉曠殑涓绉嶆柟娉曪紝鏁欑▼搴斿湪涓瀹氱Н鍒閮ㄥ垎銆傛渶绠鍗曠殑绉垎鏄鐓у叕寮忥紝浣嗘垜浠湁鏃堕渶瑕佺Н鍒嗙殑寮忓瓙銆備笌鍏紡涓嶅悓锛屼絾鏈変簺鐩镐技锛岃繖鏃讹紝鎴戜滑鍙互鑰冭檻锛屾槸鍚︽妸dx鍙樻崲鎴恉u鐨勫舰寮忥紝锛籾锛漟锛坸锛夛冀鎶婄Н鍒嗗紡涓殑x鐨勭殑鍑芥暟锛屽彉鎹㈡垚u鐨勫嚱鏁帮紝浣跨Н鍒嗗紡绗﹀悎鍏紡褰㈠紡銆傝繖鏍凤紝灏卞緢鏂逛究鐨勮繘琛岀Н鍒嗭紝鍐...
