求这道不定积分答案及过程 求这道题的不定积分
\u4e00\u9053\u6c42\u4e0d\u5b9a\u79ef\u5206\u7684\u9898\u76ee\u80fd\u591f\u6709\u591a\u4e2a\u7b54\u6848\u5417\u697c\u4e3b\u8bf4\u5bf9\u4e86\u4e00\u534a\uff1a
1\u3001\u4e0d\u5b9a\u79ef\u5206\u7684\u7ed3\u679c\uff0c\u786e\u5b9e\u4f1a\u6709\u4e0d\u540c\u7684\u7b54\u6848\u3002\u4f46\u662f\uff0c\u6240\u6709\u7684\u7b54\u6848\u90fd\u53ef\u4ee5
\u4e92\u5316\u3002\u4e0b\u9762\u7684\u7b2c\u4e00\u5f20\u56fe\u7247\uff0c\u7ed9\u4e88\u5177\u4f53\u793a\u4f8b\u3002
\u7b2c\u4e8c\u5f20\u56fe\u7247\u662f\u540c\u4e00\u4e2a\u4e0d\u5b9a\u79ef\u5206\u7684\u79ef\u5206\u7ed3\u679c\uff0c\u5b83\u4eec\u6c42\u5bfc\u540e\u662f\u76f8\u540c\u7684\u3002
.
2\u3001\u672c\u697c\u4e3b\u4e3e\u7684\u4f8b\u5b50\uff0c\u79ef\u5206\u7684\u7ed3\u679c\u662f\u53cd\u6b63\u5207\u51fd\u6570\uff0c\u800c\u7edd\u4e0d\u53ef\u80fd\u662f\u81ea\u7136\u5bf9\u6570
\u51fd\u6570\u3002\u697c\u4e3b\u5e94\u8be5\u662f\u5bf9 \u222bdx/\uff08ax + b\uff09\u7684\u79ef\u5206\u516c\u5f0f\u7406\u89e3\u9519\u4e86\u3002
.
3\u3001\u82e5\u6709\u7591\u95ee\uff0c\u6b22\u8fce\u8ffd\u95ee\uff0c\u6709\u95ee\u5fc5\u7b54\uff0c\u6709\u7591\u5fc5\u91ca\u3002
\u82e5\u70b9\u51fb\u653e\u5927\uff0c\u56fe\u7247\u5c06\u4f1a\u66f4\u52a0\u6e05\u6670\u3002
.
.
.
\u3010\u656c\u8bf7\u3011\u656c\u8bf7\u6709\u63a8\u9009\u8ba4\u8bc1\u300a\u4e13\u4e1a\u89e3\u7b54\u300b\u6743\u9650\u7684\u8fbe\u4eba\uff0c\u5343\u4e07\u4e0d\u8981\u5c06\u672c\u4eba\u5bf9\u8be5\u9898\u7684\u89e3\u7b54\u8ba4\u8bc1\u4e3a\u300a\u4e13\u4e1a\u89e3\u7b54\u300b\u3002.\u4e00\u65e6\u88ab\u8ba4\u8bc1\u4e3a\u300a\u4e13\u4e1a\u89e3\u7b54\u300b\uff0c\u6240\u6709\u7f51\u53cb\u90fd\u65e0\u6cd5\u8fdb\u884c\u8bc4\u8bba\u3001\u516c\u8bae\u3001\u7ea0\u9519\u3002\u672c\u4eba\u975e\u5e38\u9700\u8981\u503e\u542c\u5bf9\u6211\u89e3\u7b54\u7684\u5404\u79cd\u53cd\u9988\uff0c\u5373\u4f7f\u662f\u8a00\u8f9e\u6fc0\u70c8\u7684\u3001\u6279\u8bc4\u7684\u3001\u53cd\u9a73\u7684\u8bc4\u8bba\uff0c\u4e5f\u662f\u9700\u8981\u503e\u542c\u7684\u3002
.
\u8bf7\u4f53\u8c05\uff0c\u656c\u8bf7\u5207\u52ff\u8ba4\u8bc1\u3002\u8c22\u8c22\u4f53\u8c05\uff01\u8c22\u8c22\u7406\u89e3\uff01\u8c22\u8c22\uff01\u8c22\u8c22\uff01
\u7528\u5230\u4e86\u6362\u5143\u6cd5
分部积分法。
以上，请采纳。
∫x^2arctanxdx
=(1/3)∫arctanxdx^3
=(1/3)x^3arctanx-(1/3)∫x^3darctanx
=(1/3)x^3arctanx-(1/3)∫[(x^3+x)-x]/(1+x^2)dx
=(1/3)x^3arctanx-(1/3)∫xdx+(1/3)∫(x)/(1+x^2)dx
=(1/3)x^3arctanx-(1/6)x^2+(1/6)ln(1+x^2)+C
I = (1/3)∫arctanxd(x^3)
= (1/3)x^3arctanx - (1/3)∫[x^3/(1+x^2)]dx
= (1/3)x^3arctanx - (1/3)∫[(x^3+x-x)/(1+x^2)]dx
= (1/3)x^3arctanx - (1/3)∫[x-x/(1+x^2)]dx
= (1/3)x^3arctanx - (1/6)[x^2-ln(1+x^2)] + C
绛旓細杩欓 鏈夌偣楹荤儲锛屽厛鐢ㄤ笁瑙掍唬鎹紝涔嬪悗濡傜涓寮犲浘姹傚嚭(sect)^5鐨绉垎锛屽啀濡傜浜屽紶鍥炬眰鍑(sect)^3鐨勭Н鍒嗭紝鏈鍚庡彉閲忓洖浠ｃ
绛旓細鍏堢敤鍒嗛儴绉垎娉曪紝鐒跺悗鍐嶆崲鍏冿紝鍙锛漵int锛岀劧鍚庡氨鑳芥眰鍑烘潵浜嗭紝濡傚浘
绛旓細鈭玸in^2x/e^xdx =鈭1/2(1-cos2x)/e^xdx =1/2鈭(1/e^x-cos2x/e^x)dx =-1/2e^(-x)-1/2鈭玞os2x/e^xdx 瀵逛簬1/2鈭玞os2x/e^xdx 浠=e^(-x)锛宒u=-e^(-x)dx dv=cos2xdx锛寁=1/2sin2xdx 1/2鈭玞os2x/e^xdx=1/2e^(-x)*(1/2sin2x)-1/2鈭1/2sin2x[-e^(-x...
绛旓細濡傚浘銆
绛旓細銆绛旀銆慍 銆愯В鏋愩慺(1/鈭歺)=(x²+C)'=2x 浠 t=1/鈭歺锛屽垯x=1/t²鈭磃(t)=2/t²鈭磃(x)=2/x²鈭粹埆f(x)dx=鈭2/x²dx=-2/x+C
绛旓細涓嶅畾绉垎澶氶」寮忕殑鍒嗚В銆
绛旓細1銆佹湰棰樼殑绛旀鏄細D锛2銆佹湰棰樼殑绉垎鏂规硶鏄細鍑戞柟娉曪紱3銆佸叿浣绉垎杩囩▼濡備笅锛屽鏈夌枒闂紝娆㈣繋杩介棶锛屾湁闂繀绛旓紝鏈夌枒蹇呴噴锛4銆佽嫢鐐瑰嚮鏀惧ぇ锛屽浘鐗囧皢浼氭洿鍔犳竻鏅般..銆愭伋璇枫戞伋璇锋湁鎺ㄩ夎璇併婁笓涓氳В绛斻嬫潈闄愮殑杈句汉锛屽崈涓囦笉瑕佸皢鏈汉瀵硅棰樼殑瑙ｇ瓟璁よ瘉涓恒婁笓涓氳В绛斻嬨.浣犱滑涓鏃﹁璇佷负銆婁笓涓氳В绛斻嬶紝鎵鏈夌綉鍙嬮兘...
绛旓細瑙佷笅鍥撅細
绛旓細鈭(0,1) d(x²+3x)=(x²+3x) |锛0锛1锛=1+3-锛0+0锛=4
绛旓細锛1锛変护x=tant锛屽垯dx=sec^2tdt 鍘熷紡=鈭玪n(tant+sect)/sect*sec^2tdt =鈭玪n(tant+sect)*sectdt =鈭玪n(tant+sect)d[ln(tant+sect)]=(1/2)*[ln(tant+sect)]^2+C =(1/2)*[ln(x+鈭(1+x^2)]^2+C锛屽叾涓瑿鏄换鎰忓父鏁 锛2锛夊師寮=鈭玡^(sin2x-2x)*sin^2xdx =(1/2)*鈭玡...
