微积分之不定积分1题
\u5fae\u79ef\u5206\uff0c\u6c42\uff0820\uff09\u9898\u7684\u4e0d\u5b9a\u79ef\u5206\uff0c\u5b8c\u6574\u7b54\u6848dx\u4e58\u8fdb\u53bb\u5206\u5f00\u79ef\u5206\u5c31\u597d\u4e86
如图
2*(cosx)^2=(cos2x)-1
积分(cosx)^3dx=(cosx)^2dsinx
(cosx)^2+(sinx)^2=1
∫sin^2xdx+∫cos^3xdx
=∫(1-cos2x)/2dx+∫cos^2xdsinx
=x/2-(sin2x)/4+∫(1-sin^2x)dsinx
=x/2-(sin2x)/4+sinx+(sin^3x)3+C
绛旓細濡傚浘
绛旓細鏃舵斂淇℃伅涓嶅疄 鍨冨溇骞垮憡 浣庤川鐏屾按 鎴戜滑浼氶氳繃娑堟伅銆侀偖绠辩瓑鏂瑰紡灏藉揩灏嗕妇鎶ョ粨鏋滈氱煡鎮ㄣ 璇存槑 0/200 鎻愪氦 鍙栨秷 棰嗗彇濂栧姳 鎴戠殑璐㈠瘜鍊 -- 鍘荤櫥褰 鎴戠殑鐜伴噾 -- 鍘荤櫥褰 鍋氫换鍔″紑瀹濈 绱瀹屾垚 0 涓换鍔 10浠诲姟 鐣ョ暐鐣ョ暐鈥 50浠诲姟 鐣ョ暐鐣ョ暐鈥 100浠诲姟 鐣ョ暐鐣ョ暐鈥 200浠诲姟 鐣ョ暐鐣ョ暐鈥 浠诲姟鍒楄〃鍔犺浇涓......
绛旓細鏃犳硶鍒濈瓑鍙樻崲鈥︹︹﹁缁嗙瓟妗堣鍥撅紝甯屾湜鑳藉府鍒颁綘瑙ｅ喅闂
绛旓細瑙佸浘
绛旓細绉垎瀛︾殑涓昏鍐呭鍖呮嫭锛氬畾绉垎銆涓嶅畾绉垎绛夈備粠骞夸箟涓婅锛屾暟瀛﹀垎鏋愬寘鎷寰Н鍒銆佸嚱鏁拌绛夎澶氬垎鏀绉戯紝浣嗘槸鐜板湪涓鑸凡涔犳儻浜庢妸鏁板鍒嗘瀽鍜屽井绉垎绛夊悓璧锋潵锛屾暟瀛﹀垎鏋愭垚浜嗗井绉垎鐨勫悓涔夎瘝锛屼竴鎻愭暟瀛﹀垎鏋愬氨鐭ラ亾鏄寚寰Н鍒嗐備笉瀹氱Н鍒嗙殑鍏紡 1銆佲埆 a dx = ax + C锛宎鍜孋閮芥槸甯告暟 2銆佲埆 x^a dx = [x...
绛旓細鏈鏄涓嶅畾绉垎鍩烘湰璁＄畻锛屽叿浣撴楠ゅ涓嬫墍绀:鈭玼鈭(u^2-5)du =(1/2)鈭垰(u^2-5)du^2锛屽u鍑戝垎锛=(1/2)鈭垰(u^2-5)d(u^2-5)锛屽父鏁颁笉褰辩Н鍒嗙粨鏋滐紱=(1/2)鈭(u^2-5)^(1/2)d(u^2-5)锛屽箓鍑芥暟鎸囨暟鍙樺舰锛=(1/3)(u^2-5)^(3/2)+C锛屽啀娆″噾鍒嗗緱缁撴灉锛涙湰棰樿缁嗚绠...
绛旓細杩欎笁棰樻濂界敤浜嗙浜屾崲鍏绉垎娉曠殑涓夌涓嶅悓绫诲瀷銆傝缁嗙殑璇濊嚜宸卞姩鎵嬪仛鍚э細绗涓棰浠 - 1 = 鈭2sin胃 绗簩棰樹护x - 1 = 鈭2sec胃 绗笁棰樹护x - 1 = 鈭2tan胃
绛旓細瑙ｏ細f '(tanx+1)=cos²x+sec²x=1/(1+tan²x)+1+tan²x 浠=tanx+1锛屽垯tanx=t-1 f '(t)=1/[1+(t-1)²]+1+(t-1)²涓ょ鍚屾椂绉垎寰 f(t)=鈭1/[1+(t-1)²]dt +鈭玔1+(t-1)²]dt =arctan(t-1)+t+(t-1)³/...
绛旓細2.4涓夎鎹㈠厓鑴辨牴鍙凤紝浠=sinu 5.=鈭(1-lnx)*-1/(1-1/x)d1/(x-lnx)=x(1-lnx)/(1-x)(x-lnx)-鈭1/(x-lnx)dx(1-lnx)/(1-x)=x(1-lnx)/(1-x)(x-lnx)-鈭1/(x-lnx)*((1-lnx-1)(1-x)+x(1-lnx))/(1-x)²dx =x(1-lnx)/(1-x)(x-lnx)-鈭1/(1-...
绛旓細鏂规硶濡備笅锛岃浣滃弬鑰冿紝绁濆涔犳剦蹇細
