大一高数求积分，不定积分的，急求，在线等！
\u5927\u4e00\u9ad8\u6570\u6c42\u79ef\u5206\uff0c\u4e0d\u5b9a\u79ef\u5206\uff0c\u5728\u7ebf\u7b49\uff01=-1/2ln(x^2-x+1)+3/2∫1/(x^2-x+1)dx
后面一个用arctan就可以了
绛旓細鍘熷紡=-鈭(x-1/2)/(x^2-x+1)dx+3/2鈭1/(x^2-x+1)dx =-1/2ln(x^2-x+1)+3/2鈭1/(x^2-x+1)dx 鍚庨潰涓涓敤arctan灏卞彲浠ヤ簡
绛旓細鏂规硶濡備笅锛岃浣滃弬鑰冿細
绛旓細濡傚浘
绛旓細鈭玞os(鈭歺)dx 浠も垰x=u,鍒檇x/2鈭歺=du,dx=2(鈭歺)du=2udu,鍘熷紡=2鈭玼cosudu =2鈭玼d(sinu)=2[usinu-鈭玸inudu]=2(usinu+cosu)+C =2[(鈭歺)sin(鈭歺)+cos(鈭歺)]+C ~~~鈭垰x(x+1)^2dx 浠も垰x=t, 鍒檇x=2tdt锛屽甫鍏 =鈭玹(t^2+1)^2*2tdt =鈭2t^6+4t^4+2t^2dt =...
绛旓細(4x+1)^10 dx = 1/4*(4x+1)^10 d(4x-1) = 1/44*(4x+1)^11 + C 鈭 lnx/x² dx,棣栧厛灏1/x²鎺ㄨ繘d閲,杩欐槸绉垎杩囩▼= 鈭 lnx d(- 1/x),鐒跺悗浜掕皟鍑芥暟浣嶇疆= - (lnx)/x + 鈭 1/x d(lnx),灏唋nx浠巇閲屾媺鍑烘潵,杩欐槸寰垎杩囩▼= - (lnx)/x + 鈭 1/x * 1/...
绛旓細=鈭玠y/鈭歔(Cy²+1)/y²]=鈭珁*dy/鈭(Cy²+1)=1/(2C) * 鈭2C*dy/鈭(Cy²+1)=1/(2C) * 鈭玠(Cy²+1)/鈭(Cy²+1)=鈭(Cy²+1) + C'
绛旓細涔︿笂涓嶆槸鏈夌瓟妗堜箞銆傘傘備护u = tan(x/2)銆乨x = 2/(1 + u²) du銆乻inx = 2u/(1 + u²)鈭 1/(3 + sinx) dx = 鈭 1/[3 + 2u/(1 + u²)] * 2/(1 + u²) du = 鈭 (1 + u²)/[3(1 + u²) + 2u] * 2/(1 + u²)...
绛旓細鈭 x²arctanx dx = 鈭 arctanx d(x³/3)= (1/3)x³arctanx - (1/3)鈭 x³ d(arctanx)= (1/3)x³arctanx - (1/3)鈭 x³/(1 + x²) dx = (1/3)x³arctanx - (1/3)鈭 x[(1 + x²) - 1]/(1 + x&#...
绛旓細杩欓亾楂樼瓑鏁板涓嶅畾绉垎闂缁煎悎鑰冨療浜嗗井绉垎涓殑鍒嗛儴绉垎娉曘佷笁瑙掓崲鍏冩硶锛岃櫧鐒堕鐩湅璧锋潵绠鍗曪紝瑙ｉ鎬濊矾涔熷緢鏄庢櫚锛屼絾鏄噷杈鐨勮绠杈冧负澶嶆潅锛屽仛杩欑棰樺氨鐪嬭冪敓鐨勮愬績鍜岀粏蹇冪▼搴︺
绛旓細涓銆俻涓烘暣鏁帮紝鍋囧畾x=z^N锛屽叾涓璑涓哄垎鏁癿鍜宯鐨鍏垎姣嶏紱浜屻(m+1)/n涓烘暣鏁帮紝鍋囧畾a+bx^n=z^N锛屽叾涓璑鏄垎鏁皃鐨勫垎姣嶏紱涓夈俒(m+1)/n]+p涓烘暣鏁帮紝鍒╃敤浠ｆ崲锛歔ax^(-n)]+b=z^N锛屽叾涓璑涓哄垎鏁皃鐨勫垎姣嶃 璇存槑锛氫竴浜岀殑鍋囧畾鍗充负鎵浣滅殑浠ｆ崲銆傚浜庝笉鏄簩椤瑰井鍒嗗紡鐨勶紝蹇呴』鍖栧埌浜岄」寰垎寮...
