不定积分∫sin2xdx 不定积分∫sin2xdx过程
\u6c42\u4e0d\u5b9a\u79ef\u5206,\u222bsin^2x dx\u222bsin2xdx
=(1/2)\u222bsin2xd(2x)
=-(1/2)cos2x + C
∫sin2xdx=(1/2)∫sin2xd2x =-(1/2)cos2x +C 利
1/2cos2x
-(cos2x)/2
-1/2cos2x+c
绛旓細鈭sin2xdx =1/2鈭玸in2xd2x =-1/2*cos2x+C锛圕涓轰换鎰忓父鏁帮級姹傚嚱鏁癴(x)鐨涓嶅畾绉垎锛屽氨鏄姹傚嚭f(x)鐨勬墍鏈夌殑鍘熷嚱鏁帮紝鐢卞師鍑芥暟鐨勬ц川鍙煡锛屽彧瑕佹眰鍑哄嚱鏁癴(x)鐨勪竴涓師鍑芥暟锛屽啀鍔犱笂浠绘剰鐨勫父鏁癈灏卞緱鍒板嚱鏁癴(x)鐨勪笉瀹氱Н鍒嗐
绛旓細鐢变簬d -cosx=sinxdx銆傚埄鐢ㄦ崲鍏冪Н鍒嗘硶锛屽彲浠ュ緱鍒涓嶅畾绉垎 鈭玸in 2x dx =1/2 鈭玸in 2x d2x =-1/2 cos2x+C銆
绛旓細瑙ｏ細鈭(sinx)^2dx =(1/2)鈭(1-cos2x)dx =(1/2)x-(1/4)sin2x+C(C涓哄父鏁)涓嶅畾绉垎鐨勫叕寮忥細1銆佲埆adx=ax+C锛宎鍜孋閮芥槸甯告暟 2銆佲埆x^adx=[x^(a+1)]/(a+1)+C锛屽叾涓璦涓哄父鏁颁笖a鈮-1 3銆佲埆1/xdx=ln|x|+C 4銆佲埆a^xdx=(1/lna)a^x+C锛屽叾涓璦>0涓攁鈮1 5銆佲埆e^xdx=e...
绛旓細sin2xdx鐨涓嶅畾绉垎锛氣埆xsin2xdx =(-1/2)鈭玿dcos2x锛屽湪寰Н鍒嗕腑锛屼竴涓嚱鏁癴鐨勪笉瀹氱Н鍒嗭紝鎴鍘熷嚱鏁锛屾垨鍙嶅鏁帮紝鏄竴涓鏁扮瓑浜巉鐨勫嚱鏁癋锛屽嵆F鈥=f锛屼笉瀹氱Н鍒嗗拰瀹氱Н鍒嗛棿鐨勫叧绯荤敱寰Н鍒嗗熀鏈畾鐞嗙‘瀹氾紝鍏朵腑F鏄痜鐨勪笉瀹氱Н鍒嗐傛牴鎹墰椤-鑾卞竷灏艰尐鍏紡锛岃澶氬嚱鏁扮殑瀹氱Н鍒嗙殑璁＄畻灏卞彲浠ョ畝渚垮湴閫氳繃姹備笉瀹氱Н...
绛旓細鈭玸in2xdx =(1/2)鈭玸in2xd(2x)=-(1/2)cos2x + C
绛旓細瑙:(sin²x+C)'=2sinxcosx=sin2x锛鈭玸in2xdx=-鈭(-0.5sin2x)d(2x)= -0.5鈭(-sin2x)d(2x)=-0.5cos2x+C= -0.5(1-2sin²x)+C=sin²x-0.5+C C涓轰换鎰忓父鏁帮紝鍒機-0.5涔熶负浠绘剰甯告暟 鍙湁鈭玸in2xdx=sin²x+C ...
绛旓細鈭 (sinxcosx)/(sinx + cosx) dx=(1/2)(- cosx + sinx) - [1/(2鈭2)]ln|csc(x + 蟺/4) - cot(x + 蟺/4)| + C锛孋涓绉垎甯告暟銆傝В绛旇繃绋嬪涓嬶細鈭 (sinxcosx)/(sinx + cosx) dx = (1/2)鈭 (2sinxcosx)/(sinx + cosx) dx = (1/2)鈭 [(1 + 2sinxcosx) - 1]...
绛旓細鐢ㄤ簡鍑戝井鍒嗘硶(绗竴鎹㈠師娉)鈭玸in2xdx=(1/2)鈭玸in2xd2x =-(1/2)cos2x +C 鍒
绛旓細鈭玸in2xdx鐨鍘熷嚱鏁涓猴紙-1/2锛塩os2x+C銆侰涓虹Н鍒嗗父鏁般傝В绛旇繃绋嬪涓嬶細姹俿in2x鐨勫師鍑芥暟灏辨槸瀵箂in2x杩涜涓嶅畾绉垎銆傗埆sin2xdx =锛1/2锛夆埆sin2xd2x =锛-1/2锛塩os2x+C
绛旓細sin2xdx=1/2sin2xd(2x)=-1/2cos2x + C
