数学求不定积分，高手请帮忙！谢谢！
\u6570\u5b66\u6c42\u4e0d\u5b9a\u79ef\u5206\u539f\u5f0f=\u222bd(x+1)/[(x+1)²+1]
=arctan(x+1)+C
\u8fd9\u6837\u662f\u5426\u660e\u4e86\u3002
=∫(1/2)*[sin(2x+3x)+sin(2x-3x)]dx
=∫(1/2)*[sin(5x)-sin(x)]dx
=(1/2)*[-(1/5)*cos(5x)+cos(x)]+C
=(-1/10)*cos(5x)+(1/2)*cos(x)+C
其中C为任意常数。
∫sin2xcos3xdx=∫1/2(sin5x-sinx)dx
=-1/10cos5x+1/2cosx+c
∫sin2xcos3xdx
=∫1/2(sin5x-sinx)dx
=1/2(∫sin5xdx-∫sinxdx)
=1/2(1/5∫sin5xd5x-∫sinxdx)
=-(1/10)cos(5x)+(1/2)cosx+c
现场给你做的
绛旓細1.flnxdx=xlnx-fxd(lnx)=xlnx-f1dx=xlnx-x+c.2.fcos^2 xdsinx=f(1-sin^2 x)dsinx =f1dsinx-fsin^2 xdsinx =sinx-1/3 sin^3 x+c.
绛旓細棣栧厛瀵硅绉嚱鏁帮紝鐢ㄥ緟瀹氱郴鏁版硶杩涜鎷嗗垎銆傛湭瀹屽緟缁 鍒嗗埆绉垎锛娉ㄦ剰鎹㈠厓鍙樺舰銆備緵鍙傝冿紝璇风瑧绾炽
绛旓細鐢ㄤ笁瑙掍唬鎹㈠彲浠ユ眰鍑虹粨鏋溿
绛旓細浠 = tan胃锛宒x = sec²胃 d胃 鈭 (1 - x²)/鈭(1 + x²) dx = 鈭 (1 - tan²胃)/|sec胃| * (sec²胃 d胃)= 鈭 (1 - tan²胃) * sec胃 d胃 = 鈭 sec胃 d胃 - 鈭 tan²胃sec胃 d胃 = 鈭 sec胃 d胃 - 鈭 (sec²...
绛旓細鍏堢敤绉寲鍜屽樊鍏紡锛=鈭(1/2)*[sin(2x+3x)+sin(2x-3x)]dx =鈭(1/2)*[sin(5x)-sin(x)]dx =(1/2)*[-(1/5)*cos(5x)+cos(x)]+C =(-1/10)*cos(5x)+(1/2)*cos(x)+C 鍏朵腑C涓轰换鎰忓父鏁般
绛旓細璇︾粏杩囩▼濡傚浘rt鈥︹﹀笇鏈涜兘甯埌浣
绛旓細姹備笉瀹氱Н鍒 1銆傗埆sin3xcos2xdx 瑙ｏ細鍘熷紡=(1/2)鈭(sinx+sin5x)dx=(1/2)[鈭玸inxdx+(1/5)鈭玸in5xd(5x)]=(1/2)[-cosx-(1/5)cos5x]+C=-(1/2)[cosx+(1/5)cos5x]+C 2銆傛瘮杈冦1锛2銆戔埆xdx涓庛1锛2銆戔埆sinxdx鐨勫ぇ灏 瑙ｏ細銆1锛2銆戔埆xdx=(1/2)x²鈭ｃ1锛2銆=...
绛旓細1.鈭玸ec³xdx锛濃埆secxd(tanx)锛漷anxsecx锛嶁埆tan²xsecxdx 锛漷anxsecx锛嶁埆(sec²x-1)secxdx 锛漷anxsecx锛嶁埆sec³xdx锛嬧埆secxdx 鏁寸悊寰 鈭玸ec³xdx锛漑tanxsecx锛嬧埆secxdx]/2锛婥 鍏朵腑鏄撴眰鈭玸ecxdx.(浠庣暐)2.杩炵画浣跨敤鍒嗛儴绉垎娉(鎶奵os2x鍑戝井鍒,浣垮緱x²鍦ㄦ眰瀵间笅闄...
绛旓細鍥炵瓟锛氬洜涓 u=x²+2 du = d(x²+2) du = 2x dx xdx = 1/2du newmanhero 2015骞2鏈2鏃12:49:16 甯屾湜瀵逛綘鏈夋墍甯姪,鏈涢噰绾炽
绛旓細姹傝В 璁綟(x)鏄嚱鏁癴(x)鐨勪竴涓鍘熷嚱鏁帮紝鎴戜滑鎶婂嚱鏁癴(x)鐨勬墍鏈夊師鍑芥暟F(x)+ C(鍏朵腑锛孋涓轰换鎰忓父鏁帮級鍙仛鍑芥暟f(x)鐨涓嶅畾绉垎锛鍙堝彨鍋氬嚱鏁癴(x)鐨勫弽瀵兼暟锛岃浣溾埆f(x)dx鎴栬呪埆f锛堥珮绛夊井绉垎涓父鐪佸幓dx锛夛紝鍗斥埆f(x)dx=F(x)+C銆傚叾涓埆鍙仛绉垎鍙,f(x)鍙仛琚Н鍑芥暟,x鍙仛绉垎鍙橀噺,f(x)...
