高等数学不定积分怎么做 高数不定积分，要怎么做？详细点
\u9ad8\u6570\u4e0d\u5b9a\u79ef\u5206 \u8bf7\u95ee\u7528\u51d1\u5fae\u5206\u6cd5\u600e\u4e48\u505a\uff1f\u5148\u628a\u88ab\u79ef\u51fd\u6570\u62c6\u5206\u4e3a\u7b80\u5355\u7684\u4e24\u9879\u518d\u51d1\u5fae\u5206\uff1a
\u4e09\u89d2\u6362\u5143\u8131\u6839\u53f7\uff0c\u6362\u5143x=sinu\uff0c
=\u222b(-\u03c0/2\u5230\u03c0/2)sin²ucos²udu
=1/4\u222bsin²2udu
=1/8\u222b(1-cos4u)du
=\u03c0/8
如图
原式=1/2 ∫1/(x²-1/2)dx
=1/2 ∫1/(x²-(√2/2)²)dx
=1/2*1/(2×√2/2)×ln|(x-√2/2)/(x+√2/2)|+c
=√2/4ln|(2x-√2)/(2x+√2)|+c
绛旓細- 1) + B/(x + 1)锛岀劧鍚庤В鍑篈鍙夿 绗簩锛氫竾鑳藉叕寮忥紝瀵逛簬鍒嗗紡鏈変笁瑙掑嚱鏁版椂鐢ㄥ埌锛屼富瑕佸皢涓夎鍑芥暟鍖栦负鏈夌悊鍑芥暟鍚庡啀绉垎 浠 = tan(x/2)锛宒x = 2du/(1 + u²)锛宻inx = 2u/(1 + u²)锛宑osx = (1 - u²)/(1 + u²)濡傛灉鏄瀹氱Н鍒鐨勮瘽灏辨洿澶氭洿闅句簡銆
绛旓細=鈭玡^(2x)路(tan²x+2tanx+1)dx =鈭玡^(2x)路(sec²x+2tanx)dx =鈭玡^(2x)路sec²xdx+鈭玡^(2x)路2tanxdx =鈭玡^(2x)路d(tanx)+鈭玡^(2x)路2tanxdx =e^(2x)路tanx-鈭玡^(2x)路2tanxdx+鈭玡^(2x)路2tanxdx =e^(2x)路tanx+C ...
绛旓細鏂规硶涓锛屾崲鍏冩硶锛氭柟娉曚簩锛屽垎閮绉垎娉 浠ヤ笂锛岃閲囩撼銆
绛旓細瓒呰秺绉垎瓒呰秺绉垎(閫氬父涔熺О涓轰笉鍙Н),涔熷氨鏄杩欎釜绉垎鐨鍘熷嚱鏁涓嶈兘鐢ㄦ垜浠墍瀛︾殑浠讳綍涓绉嶅嚱鏁版潵琛ㄧず.浣嗗鏋滃紩鍏ユ柊鐨勫嚱鏁癳rf(x)=鈭玔0,x]e^(-t^2)dt,閭ｄ箞璇ュ嚱鏁扮殑绉垎灏卞彲琛ㄧず涓篹rf(x)+c.閬撶悊寰堢畝鍗,姣斿鈭玿^ndx,涓鑸殑璇ョН鍒嗕负1/(n+1)x^(n+1),濡傛灉涓嶅紩鍏nx,閭ｄ箞鈭1/xdx灏变笉鍙Н...
绛旓細18棰橈紝鍙湁鎹㈠厓浜嗭紝璁綼rctan鈭歺=u锛屽垯x=tan²u锛岀劧鍚庡噾寰垎锛屽鍥 2棰橈紝寮勬竻鍘熷嚱鏁涓庡鍑芥暟鐨勫叧绯诲嵆鍙
绛旓細濡傚浘
绛旓細鍘熷紡=1/2*鈭2(x+1-2)dx/(x²+2x+3)=1/2*鈭(2x+2)dx/(x²+2x+3)-1/2*鈭4dx/(x²+2x+3)=1/2*鈭玠(x²+2x+3)/(x²+2x+3)-2鈭玠(x+1)/[(x+1)²+2]=1/2*ln|x²+2x+3|-鈭2*arctan[(x+1)/鈭2]+C ...
绛旓細杩欎釜搴旇寰堝鏄撳惂 鈭玹an^4 xdx =鈭(sec^2 x-1)tan^2 xdx =鈭玸ec^2 x*tan^2 xdx-鈭玹an^2 xdx =鈭*tan^2 xdtanx-鈭(sec^2 x-1)dx =1/3tan^3 x-tanx+x+C
绛旓細闅愬嚱鏁涓嶅畾绉垎锛屽彲浠ラ噰鐢ㄦ瀬鍧愭爣浠ｆ崲锛屾垨鑰呭叾浠栦唬鎹紝鎶妜鍜寉閮戒唬鎹负胃鐨勫嚱鏁般傚鏋滄柟绋婩(x,y)=0鑳界‘瀹歽鏄痻鐨勫嚱鏁帮紝閭ｄ箞绉拌繖绉嶆柟寮忚〃绀虹殑鍑芥暟鏄殣鍑芥暟銆傝屽嚱鏁板氨鏄寚锛氬湪鏌愪竴鍙樺寲杩囩▼涓紝涓や釜鍙橀噺x銆亂锛屽浜庢煇涓鑼冨洿鍐呯殑x鐨勬瘡涓涓硷紝y閮芥湁纭畾鐨勫煎拰瀹冨搴旓紝y灏辨槸x鐨勫嚱鏁般傚浜庝竴涓凡缁忕‘瀹...
绛旓細浠=鈭(x²+1)a²=x²+1 2ada=2xdx 鎵浠2ada/x²=2dx/x 鍗砫x/x=ada/(a²-1)鎵浠ュ師寮=鈭玜²da/(a²-1)=鈭玔1+1/(a²-1)]da =鈭珄1+1/2[1/(a-1)-1/(a+1)]}da =a+1/2ln[(a-1)/(a+1)]+C =鈭(x²+1)+...
