求不定积分∫1/（1+³✔（x+1））dx 高等数学中,o(x)是什么意思?
\u9ad8\u7b49\u6570\u5b66\u90fd\u5b66\u4ec0\u4e48\uff1f\u9ad8\u7b49\u6570\u5b66\u4e3b\u8981\u5185\u5bb9\u5305\u62ec\uff1a\u6781\u9650\u3001\u5fae\u79ef\u5206\u3001\u7a7a\u95f4\u89e3\u6790\u51e0\u4f55\u4e0e\u5411\u91cf\u4ee3\u6570\u3001\u7ea7\u6570\u3001\u5e38\u5fae\u5206\u65b9\u7a0b\u3002
\u6307\u76f8\u5bf9\u4e8e\u521d\u7b49\u6570\u5b66\u800c\u8a00\uff0c\u6570\u5b66\u7684\u5bf9\u8c61\u53ca\u65b9\u6cd5\u8f83\u4e3a\u7e41\u6742\u7684\u4e00\u90e8\u5206\u3002
\u5e7f\u4e49\u5730\u8bf4\uff0c\u521d\u7b49\u6570\u5b66\u4e4b\u5916\u7684\u6570\u5b66\u90fd\u662f\u9ad8\u7b49\u6570\u5b66\uff0c\u4e5f\u6709\u5c06\u4e2d\u5b66\u8f83\u6df1\u5165\u7684\u4ee3\u6570\u3001\u51e0\u4f55\u4ee5\u53ca\u7b80\u5355\u7684\u96c6\u5408\u8bba\u521d\u6b65\u3001\u903b\u8f91\u521d\u6b65\u79f0\u4e3a\u4e2d\u7b49\u6570\u5b66\u7684\uff0c\u5c06\u5176\u4f5c\u4e3a\u4e2d\u5c0f\u5b66\u9636\u6bb5\u7684\u521d\u7b49\u6570\u5b66\u4e0e\u5927\u5b66\u9636\u6bb5\u7684\u9ad8\u7b49\u6570\u5b66\u7684\u8fc7\u6e21\u3002
\u901a\u5e38\u8ba4\u4e3a\uff0c\u9ad8\u7b49\u6570\u5b66\u662f\u7531\u5fae\u79ef\u5206\u5b66\uff0c\u8f83\u6df1\u5165\u7684\u4ee3\u6570\u5b66\u3001\u51e0\u4f55\u5b66\u4ee5\u53ca\u5b83\u4eec\u4e4b\u95f4\u7684\u4ea4\u53c9\u5185\u5bb9\u6240\u5f62\u6210\u7684\u4e00\u95e8\u57fa\u7840\u5b66\u79d1\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u9ad8\u7b49\u6570\u5b66\u8bfe\u7a0b\u5206\u4e3a\u4e24\u4e2a\u5b66\u671f\u8fdb\u884c\u5b66\u4e60\u3002\u5b83\u7684\u6559\u5b66\u5185\u5bb9\u5305\u542b\u4e86\u4e00\u5143\u51fd\u6570\u5fae\u79ef\u5206\u3001\u591a\u5143\u51fd\u6570\u5fae\u79ef\u5206\u3001\u7a7a\u95f4\u89e3\u6790\u51e0\u4f55\u4e0e\u5411\u91cf\u4ee3\u6570\u521d\u6b65\u3001\u5fae\u5206\u65b9\u7a0b\u521d\u6b65\u3001\u573a\u8bba\u521d\u6b65\u7b49\u3002
\u5728\u5b66\u4e60\u8fd9\u4e9b\u9ad8\u7b49\u6570\u5b66\u7684\u5185\u5bb9\u7684\u65f6\u5019\uff0c\u5f88\u591a\u7684\u540c\u5b66\u8868\u793a\u72af\u96be\uff0c\u7684\u786e\uff0c\u56e0\u4e3a\u8fd9\u4e9b\u90fd\u662f\u5728\u9ad8\u4e2d\u8bfe\u7a0b\u7684\u57fa\u7840\u4e0a\u5b8c\u5584\u7684\uff0c\u60f3\u8981\u66f4\u597d\u7684\u5b66\u597d\u9ad8\u7b49\u6570\u5b66\u8fd9\u95e8\u5b66\u79d1\uff0c\u5728\u9ad8\u4e2d\u65f6\u5019\u7684\u79ef\u7d2f\u663e\u5f97\u7279\u522b\u7684\u91cd\u8981\u3002
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u2014\u9ad8\u7b49\u6570\u5b66
o(x)\u662f\u9ad8\u9636\u65e0\u7a77\u5c0f\u3002
\u5728\u540c\u4e00\u4e2a\u53d8\u5316\u8fc7\u7a0b\u4e2d\u7684\u4e24\u4e2a\u65e0\u7a77\u5c0f\uff0c\u867d\u7136\u540c\u65f6\u90fd\u8d8b\u5411\u4e8e\u96f6\uff0c\u4f46\u662f\u5b83\u4eec\u8d8b\u5411\u4e8e\u96f6\u7684\u5feb\u6162\u7a0b\u5ea6\u6709\u65f6\u5374\u4e0d\u4e00\u6837\uff0c\u751a\u81f3\u5dee\u522b\u5f88\u5927\u3002\u5b9e\u9645\u95ee\u9898\u4e2d\uff0c\u6709\u65f6\u9700\u8981\u8ba8\u8bba\u8fd9\u79cd\u8d8b\u5411\u96f6\u7684\u5feb\u6162\u95ee\u9898\u3002
\u82e5lim(\u03b2/\u03b1)=0\uff0c\u5219\u79f0\u201c\u03b2\u662f\u6bd4\u03b1\u8f83\u9ad8\u9636\u7684\u65e0\u7a77\u5c0f\u201d\u3002\u610f\u601d\u662f\u5728\u67d0\u4e00\u8fc7\u7a0b(x\u2192x0\u6216x\u2192\u221e\u8fd9\u7c7b\u8fc7\u7a0b)\u4e2d\uff0c\u03b2\u21920\u6bd4\u03b1\u21920\u5feb\u4e00\u4e9b \u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u65e0\u7a77\u6216\u65e0\u9650\uff0c\u6570\u5b66\u7b26\u53f7\u4e3a\u221e\u3002\u6765\u81ea\u4e8e\u62c9\u4e01\u6587\u7684\u201cinfinitas\u201d\uff0c\u5373\u201c\u6ca1\u6709\u8fb9\u754c\u201d\u7684\u610f\u601d\u3002\u5b83\u5728\u795e\u5b66\u3001\u54f2\u5b66\u3001\u6570\u5b66\u548c\u65e5\u5e38\u751f\u6d3b\u4e2d\u6709\u7740\u4e0d\u540c\u7684\u6982\u5ff5\u3002\u901a\u5e38\u4f7f\u7528\u8fd9\u4e2a\u8bcd\u7684\u65f6\u5019\u5e76\u4e0d\u6d89\u53ca\u5b83\u7684\u66f4\u52a0\u6280\u672f\u5c42\u9762\u7684\u5b9a\u4e49\u3002
\u5728\u795e\u5b66\u65b9\u9762\uff0c\u4f8b\u5982\u5728\u50cf\u795e\u5b66\u5bb6\u9093\u65af\u00b7\u53f8\u5404\u8131\uff08Duns Scotus\uff09\u7684\u8457\u4f5c\u4e2d\uff0c\u4e0a\u5e1d\u7684\u65e0\u9650\u80fd\u91cf\u662f\u8fd0\u7528\u5728\u65e0\u7ea6\u675f\u4e0a\uff0c\u800c\u4e0d\u662f\u8fd0\u7528\u5728\u65e0\u9650\u91cf\u4e0a\u3002\u5728\u54f2\u5b66\u65b9\u9762\uff0c\u65e0\u7a77\u53ef\u4ee5\u5f52\u56e0\u4e8e\u7a7a\u95f4\u548c\u65f6\u95f4\u3002\u5728\u795e\u5b66\u548c\u54f2\u5b66\u4e24\u65b9\u9762\uff0c\u65e0\u7a77\u53c8\u4f5c\u4e3a\u65e0\u9650\uff0c\u5f88\u591a\u6587\u7ae0\u90fd\u63a2\u8ba8\u8fc7\u65e0\u9650\u3001\u7edd\u5bf9\u3001\u4e0a\u5e1d\u548c\u829d\u8bfa\u6096\u8bba\u7b49\u7684\u95ee\u9898\u3002
\u5728\u6570\u5b66\u65b9\u9762\uff0c\u65e0\u7a77\u4e0e\u4e0b\u8ff0\u7684\u4e3b\u9898\u6216\u6982\u5ff5\u76f8\u5173\uff1a\u6570\u5b66\u7684\u6781\u9650\u3001\u963f\u5217\u592b\u6570\u3001\u96c6\u5408\u8bba\u4e2d\u7684\u7c7b\u3001\u6234\u5fb7\u91d1\u7684\u65e0\u9650\u7fa4\u3001\u7f57\u7d20\u6096\u8bba\u3001\u8d85\u5b9e\u6570\u3001\u5c04\u5f71\u51e0\u4f55\u3001\u6269\u5c55\u7684\u5b9e\u6570\u8f74\u4ee5\u53ca\u7edd\u5bf9\u65e0\u9650\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u9ad8\u9636\u65e0\u7a77\u5c0f
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u65e0\u7a77\u5927
令³√(x+1)=t，则x=t³-1
∫1/[(1+³√(x+1)] dx
=∫[1/[(1+t)]d(t³-1)
=∫[2t²/[(1+t)]dt
=∫[(2t²+2t-2t-2+2)/[(1+t)]dt
=∫[2t-2 +2)/[(1+t)]dt
=∫(2t-2)dt+ 2∫[1/[(1+t)]d(1+t)
=t²-2t +2ln|1+t|+C
=[³√(x+1)]² -2³√(x+1)+2ln|1+³√(x+1)| +C
绛旓細鎴戠殑 涓嶅畾绉垎1鍜姹 涓嶅畾绉垎1鍜嬫眰... 涓嶅畾绉垎1鍜嬫眰 灞曞紑 鎴戞潵绛 1涓洖绛 #鐑# 涓轰粈涔堢幇鍦ㄦ儏鏅枩鍓ц秺鏉ヨ秺灏戜簡? wjl371116 2017-12-08 路 鐭ラ亾鍚堜紮浜烘暀鑲茶瀹 wjl371116 鐭ラ亾鍚堜紮浜烘暀鑲茶瀹 閲囩撼鏁:15454 鑾疯禐鏁:65385 鍚慣A鎻愰棶 绉佷俊TA 鍏虫敞 灞曞紑鍏ㄩ儴 鏈洖绛旂敱鎻愰棶鑰呮帹鑽 宸茶禐杩 ...
绛旓細鎴戠殑 姹備笉瀹氱Н鍒1 3涓洖绛 #璇濋# 鎵撳伐浜哄繀鐪嬬殑鑱屽満銆庣淮鏉冦忔寚鍗!fnxnmn 2014-12-09 路 TA鑾峰緱瓒呰繃5.8涓囦釜璧 鐭ラ亾澶ф湁鍙负绛斾富 鍥炵瓟閲:1.1涓 閲囩撼鐜:14% 甯姪鐨勪汉:1浜 鎴戜篃鍘荤瓟棰樿闂釜浜洪〉 鍏虫敞 灞曞紑鍏ㄩ儴 鏇村杩介棶杩界瓟 杩界瓟 鏈洖绛旂敱鎻愰棶鑰呮帹鑽 宸茶禐杩 宸茶俯杩< 浣犲杩欎釜鍥炵瓟鐨勮瘎...
绛旓細=ln(鈭((1+胃)/(1-胃)))+C =ln|sect锛媡ant|锛婥 =lnl鈭(1+tan^2t)+tantl+c =lnl鈭(1+x^2)+xl+c
绛旓細缁忔祹鏁板鍥㈤槦涓轰綘瑙ｇ瓟锛屾弧鎰忚閲囩撼锛
绛旓細2019-05-08 涓嶅畾绉垎 鈭1/(1+e^x)dx瑙ｆ硶? 21 2017-12-04 涓嶅畾绉垎鈭1/(1-2x)dx 24 2014-02-18 澶т竴涓嶅畾绉垎闂,鈭1/(m+nx)dx(m銆乶涓哄凡鐭ュ父鏁)... 1 2013-01-07 姹備笉瀹氱Н鍒嗏埆1/(1+t)dx 2 2020-05-28 涓嶅畾绉垎棰 鈭1/cosxdx? 2018-09-24 涓嶅畾绉垎:鈭 1/(1-x^3) dx...
绛旓細鈭1/(1+e^x)dx =鈭紙1+e^x-e^x锛/(1+e^x)dx =鈭1dx-鈭紙e^x锛/(1+e^x)dx =x-鈭1/(1+e^x)d锛坋^x锛=x-鈭1/(1+e^x)d锛1+e^x锛=x-ln锛1+e^x锛+C
绛旓細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銆鈭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^x+C 6銆佲埆cosxdx=sinx+C 7銆佲埆sinxdx=-cosx+C 8銆佲埆cotxdx=ln|sinx|+C=-ln...
绛旓細瑙ｏ細浠³鈭(x+1)=t锛屽垯x=t³-1 鈭1/[(1+³鈭(x+1)] dx =鈭玔1/[(1+t)]d(t³-1)=鈭玔2t²/[(1+t)]dt =鈭玔(2t²+2t-2t-2+2)/[(1+t)]dt =鈭玔2t-2 +2)/[(1+t)]dt =鈭(2t-2)dt+ 2鈭玔1/[(1+t)]d(1+t)=t²-...
绛旓細鏈嬪弸锛屾偍濂斤紒璇︾粏杩囩▼濡傚浘rt鎵绀猴紝甯屾湜鑳藉府鍒颁綘瑙ｅ喅浣犲績涓殑闂
绛旓細瀹為檯涓婏紝鍐欏埌鍊掓暟绗簩姝ュ氨鍙互浜嗐備互涓婏紝璇烽噰绾炽
