常用函數(shù)積分表增強(qiáng)版-資料下載頁(yè)
2025-06-29 11:49本頁(yè)面
【正文】 =coshaxan1sinhn1axn2n1dxsinhn2ax，n≠1244. dxcoshnax=sinhaxan1coshn1ax+n2n1dxcoshn2ax，n≠1245. coshnaxsinhmaxdx=coshn1axanmsinhm1ax+n1nmcoshn2axsinhmaxdx=coshn+1axam1sinhm1ax+nm+2m1coshnaxsinhm2axdx+C=coshn1axam1sinhm1ax+n1m1coshn2axsinhm2axdx+C，m≠n,m≠1246. sinhmaxcosnaxdx=sinhm1axamncoshn1ax+m1mnsinhm2axcoshnaxdx+C=sinhm+1axan1coshn1ax+mn+2n1sinhmaxcoshn2axdx+C=sinhm1axan1coshn1ax+m1n1sinhm2axcoshn2axdx+C，m≠n,n≠1247. xsinhaxdx=1axcoshax1a2sinhax+C248. xcoshaxdx=1axsinhax1a2coshax+C249. tanhaxdx=1alncoshax+C250. cothaxdx=1alnsinhax+C251. tanhnaxdx=tanhn1axan1+tanhn2axdx+C，n≠1252. cothnaxdx=cothn1axan1+cothn2axdx，n≠1253. sinhaxsinhbxdx=asinhbxcoshaxbcoshbxsinhaxa2b2+C254. coshaxcosbxdx=asinhaxcoshbxbsinhbxcoshaxa2b2+C255. coshaxsinhbxdx=asinhaxsinhbxbcoshaxcoshbxa2b2+C256. sinhax+bsincx+ddx=aa2+c2coshax+bsincx+dca2+c2sinhax+bcoscx+d+C257. sinhax+bcoscx+ddx=aa2+c2coshax+bcoscx+d+ca2+c2sinhax+bsincx+d+C258. coshax+bsincx+ddx=aa2+c2sinhax+bsincx+dca2+c2coshax+bcoscx+d+C259. coshax+bcoscx+ddx=aa2+c2sinhax+bcoscx+d+ca2+c2coshax+bsincx+d+C260. arcsinhxadx=xarcsinhxax2+a2+C261. arccoshxadx=xarccoshxax2a2+C262. arctanhxadx=xarctanhxa+a2lna2x2+C，xa263. arccothxadx=xarccothxa+a2lnx2a2+C，xa264. arcsechxadx=xarcsechxaaarctanxaxa+xxa+C，x∈0,a265. arccschxadx=xarccschxa+alnx+x2+a2a+C，x∈0,a266. xeaxdx=eaxa2ax1+C，a≠0267. baxdx=baxa lnb+C，a≠0，b0，b≠1268. x2eaxdx=eaxx2a2xa2+2a3+C269. xneaxdx=xneaxanaxn1eaxdx，a≠0270. eaxdxx=lnx+i=1∞axiii!+C271. eaxdxxn=1n1eaxxn1+aeaxxn1dx+C，n≠1272. eaxlnxdx=1aeaxlnxEiax+C273. eaxsinbxdx=eaxa2+b2asinbxbcosbx+C274. eaxcosbxdx=eaxa2+b2acosbx+bsinbx+C275. eaxsinnbxdx=eaxsinn1xa2+n2asinxncosx+nn1a2+n2eaxsinn2xdx276. eaxcosnbxdx=eaxcosn1xa2+n2acosx+nsinx+nn1a2+n2eaxcosn2xdx277. xeax2dx=12aeax2+C278. 1σ2πexμ22σ2dx=12σ1+erfxμ2σ+C279. ex2dx=ex2j=0n1a2jx2j+1+2n1a2n2ex2x2ndx，n0 其中a2j=1352j12j+1=2j!j!22j+1+C280. ∞∞eax2dx=πa the Gaussian integral281. 0∞x2nex2a2dx=π2n!n!a22n+1282. lnaxdx=xlnaxx+C283. lnx2dx=xlnx22xlnx+2x+C284. lnaxndx=xlnaxnnlnaxn1dx285. dxlnx=lnlnx+lnx+i=2∞lnxiii!+C286. dxlnxn=xn1lnxn1+1n1dxlnxn1+C，n≠1287. xmlnxdx=xm+1lnxm+11m+12+C，n≠1288. xmlnxndx=xm+1lnxnm+1nm+1xmlnxn1dx+C，m≠1289. lnxndxx=lnxn+1n+1+C，n≠1290. lnxdxxm=lnxm1xm11m12xm1，m≠1291. lnxndxxm=lnxnm1xm1+nm1lnxn1dxxm，m≠1292. xmdxlnxn=xm+1n1lnxn1+m+1n1xmdxlnxn1，n≠1293. xnlnaxmdx=xn+1lnaxmn+1mn+1xnlnaxm1dx，n≠1294. lnaxmxdx=lnaxm+1m+1+C，m≠1295. dxxlnax=lnlnax+C296. dxxnlnx=lnlnx+i=1∞1in1ilnxiii!+C297. dxxlnxn=1n1lnxn1，n≠1298. sinlnxdx=x2sinlnxcoslnx+C299. coslnxdx=x2sinlnx+coslnx+C300. exxlnxx1xdx=exxlnxxlnx+C17
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