求三角函数sec的不定积分过程,
∫secxdx=∫dx/cosx=∫cosxdx/cos^2(x)=∫d(sinx)/[(1+sinx)(1-sinx)]=1/2∫(1/(1+sinx)+1/(1-sinx))d(sinx)=1/2ln|1+sinx|-1/2ln|1-sinx|+C=ln√((1+sinx)/(1-sinx))+C=ln|(1+sinx)/cosx|+C=ln|secx+tanx|+C绛旓細鈭玸ecxdx=鈭玠x/cosx=鈭玞osxdx/cos^2(x)=鈭玠(sinx)/[(1+sinx)(1-sinx)]=1/2鈭(1/(1+sinx)+1/(1-sinx))d(sinx)=1/2ln|1+sinx|-1/2ln|1-sinx|+C=ln鈭((1+sinx)/(1-sinx))+C=ln|(1+sinx)/cosx|+C=ln|secx+tanx|+C ...
绛旓細绗竴绉嶆渶蹇細鈭 secx dx = 鈭 secx • (secx + tanx)/(secx + tanx) dx = 鈭 (secxtanx + sec²x)/(secx + tanx) dx = 鈭 d(secx + tanx)/(secx + tanx)= ln|secx + tanx| + C 绗簩绉嶏細鈭 secx dx = 鈭 1/cosx dx = 鈭 cosx/cos²x dx = 鈭 d...
绛旓細=ln(secx+tanx|+C=鍙宠竟 绉垎鍏紡涓昏鏈夊涓嬪嚑绫伙細鍚玜x+b鐨勭Н鍒嗐佸惈鈭(a+bx)鐨勭Н鍒嗐佸惈鏈墄^2卤伪^2鐨勭Н鍒嗐佸惈鏈塧x^2+b(a>0)鐨勭Н鍒嗐佸惈鏈夆垰(a²+x^2) (a>0)鐨勭Н鍒嗐佸惈鏈夆垰(a^2-x^2) (a>0)鐨勭Н鍒嗐佸惈鏈夆垰(|a|x^2+bx+c) (a鈮0)鐨勭Н鍒嗐佸惈鏈涓夎鍑芥暟鐨勭Н鍒銆佸惈鏈夊弽...
绛旓細1銆佸皢tan⁴x闄嶉樁锛屽彲杩愮敤涓夎鍑芥暟鐨鍩烘湰鍏崇郴sec²x=tan²x+1杩涜鍖栫畝 2銆佷护u=tanx锛岃繘琛屼笁瑙掍唬鎹紝灏嗗叾绠鍖栵紝鍐嶆寜鍩烘湰绉垎鍏紡杩涜璁＄畻銆3銆佸皢鍙橀噺鍥炰唬锛屾渶鍚庡緱鍒伴棶棰樼殑缁撴灉 銆姹傝В杩囩▼銆戙愭湰棰樼煡璇嗙偣銆1銆涓嶅畾绉垎銆傝f(x)鍦ㄦ煇鍖洪棿I涓婃湁瀹氫箟锛屽鏋滃瓨鍦ㄥ嚱鏁癋(x)锛屼娇寰楀浜庝换...
绛旓細涓夎鍑芥暟鐨勪笉瀹氱Н鍒閫氬父鍙互閫氳繃浠ヤ笅鏂规硶璁＄畻锛1. 鍩烘湰涓夎鍑芥暟鐨勪笉瀹氱Н鍒嗭細- sin(x)dx锛氣埆sin(x)dx = -cos(x) + C 锛堝叾涓瑿涓哄父鏁帮級- cos(x)dx锛氣埆cos(x)dx = sin(x) + C - tan(x)dx锛氣埆tan(x)dx = log_|tan(x)| + C - sec(x)dx锛氣埆sec(x...
绛旓細x_-1锛夆攤+C銆傚父瑙佺殑涓夎鍑芥暟鏈夊叚涓細sinx锛宑osx锛宼anx锛宑scx锛宻ecx锛宑otx锛屽叾涓櫎浜唖inx鍜宑osx澶栵紝鍏跺畠鍥涗釜鍑芥暟鐨勪笉瀹氱Н鍒嗛兘涓嶆槸鍙互寰堝鏄撴眰鍑虹殑锛屽彲鍒╃敤绗竴绫绘崲鍏冩硶鏉ユ帹瀵煎叾瀹冨洓涓涓夎鍑芥暟鐨勪笉瀹氱Н鍒鍏紡锛屽叾涓』瑕佺敤鍒拌繖浜涗笁瑙掑嚱鏁扮殑瀵兼暟鍏紡锛屼互鍙婁竴浜涘父鐢ㄧ殑涓夎鎭掔瓑寮忥紝渚嬪鍊嶈鍏紡绛夈
绛旓細璁＄畻锛坱anx锛²涓嶅畾绉垎鐨勬柟娉曪細锛坱anx锛²=鈭玔(secx)^2-1]dx =鈭(secx)^2dx-x =tanx-x+c
绛旓細dx = sec²胃 d胃 鈭 dx/(x²+1)^(3/2)= 鈭 (sec²胃)/(tan²胃+1)^(3/2) d胃 = 鈭 (sec²胃)/(sec²胃)^(3/2) d胃 = 鈭 (sec²胃)/(sec³胃) d胃 = 鈭 cos胃 d胃 = sin胃 + C = x/鈭(1+x²) + C ...
绛旓細绉垎 sec^3 t dt =sec t tan t +ln|sec t+tant | 锛5锛夌Н鍒 sec^3 t dt =1/2*[sec t tan t +ln|sec t+tant |]+C 锛6锛夌劧鍚庡氨寰椾唬浼氬幓锛寈=tan t, sec t= 鏍瑰彿(1+tan^2 t)=鏍瑰彿(1+x^2)绉垎=1/2*[ x*鏍瑰彿(1+x^2)+ln|x + 鏍瑰彿(1+x^2)| ]+C ...
绛旓細鍘熷紡=鈭sec³ada =鈭玸ecadtana =secatana-鈭玹anadseca =secatana-鈭玹ana路tanasecada =secatana-鈭(sec²a-1)secada =secatana-鈭(sec³a-seca)da 鎵浠 2鍘熷紡=secatana+鈭玸ecada =secatana+ln|seca+tana|+2c 鎵浠 鍘熷紡=1/2secatana+1/2ln|seca+tana|+c ...
