3.14 Integrals 1301 to 1400

  3.14.1 2x3+e2(3x2+(16+4x)log(x))x2(328xx2+(64+8x)log(x))x2dx
  3.14.2 1200015601x12e45(1+5x)x3960x2372x312x4+e35(1+5x)(12372x36x2)+e25(1+5x)(3603996x756x236x3)+e15(1+5x)(360016320x4356x2396x312x4)+(36004320x36e35(1+5x)x756x236x3+e25(1+5x)(36756x72x2)+e15(1+5x)(7204392x792x236x3))log(x)+(360396x36e25(1+5x)x36x2+e15(1+5x)(36396x36x2))log2(x)+(1212x12e15(1+5x)x)log3(x)xdx
  3.14.3 1+xxdx
  3.14.4 10x+15x2+10x4+28x5+7x6+2x8+14x9+(10x+20x4+6x5+12x8)log(1+2x3x2)1+2x3dx
  3.14.5 6x2+6x3+(216+1296x+54x2396x3)log(x)+(108648x9x2+210x3)log(x)log(log(x))+(18+108x36x3)log(x)log2(log(x))+(16x+2x3)log(x)log3(log(x))(216432x216x2)log(x)+(108+216x+108x2)log(x)log(log(x))+(1836x18x2)log(x)log2(log(x))+(1+2x+x2)log(x)log3(log(x))dx
  3.14.6 e164e34x((22x2xlog(x))log(x1x)+(14x)log2(x1x))dx
  3.14.7 10040e2+4e4x3+(10x4+2x5)log(x)+x5log2(x)x5dx
  3.14.8 3e5+2e5+2x+e5+x(52x)+e5+xxlog(x)4x+8exx+4e2xx+(4x8exx4e2xx)log(x)+(x+2exx+e2xx)log2(x)dx
  3.14.9 x3+2ee2x+2xx34log(x2)+2log2(x2)x3dx
  3.14.10 1+x+ex(2x2+x3)+6xlog(ex+exx2x)xlog(ex+exx2x)dx
  3.14.11 e13xlog2(x+x2)((9+18x)log(x)+(3+3x+(99x2)log(x))log(x+x2))x4+x5dx
  3.14.12 (8e4x12x2log(2e3))log(log(5))dx
  3.14.13 5+10ex2x+e5+e36x4(1+2ex2x+e36x4(288x3144ex2x3144x4))25+10e5+e36x4+e10+2e36x4dx
  3.14.14 e6400220x+4x21280x3+172x44x5+64x615x7+x8+(6400860x+20x2640x3+150x410x5)log(2)+(1600375x+25x2)log2(2)10020x3+x6+(10010x3)log(2)+25log2(2)(2200+80x+5780x3184x4706x6+76x7+15x92x10+(9700+440x+5140x3520x4225x6+30x7)log(2)+(8050+700x+1125x3150x4)log2(2)+(1875+250x)log3(2))1000300x3+30x6x9+(1500300x3+15x6)log(2)+(75075x3)log2(2)+125log3(2)dx
  3.14.15 14(eex(1+ex(64x))+80x)dx
  3.14.16 2099280852x+116568x274529x3+17820x4+(10512+35460x43308x2+22248x33888x4)log(x)+(12963888x+3888x21296x3)log2(x)8x3+24x424x5+8x6dx
  3.14.17 50log2(3)+e8xlog(x2)log3(5log(x2))25xlog2(3)log(x2)log(5log(x2))+e8x2log(x2)log3(5log(x2))dx
  3.14.18 ex(exx2+e1eeex(x+exx6)+x2x(ex(1+x2)+eeex(x+exx6)(ex+eex(x+exx6)(xx26exx6))))x2dx
  3.14.19 2561+256xdx
  3.14.20 240x+120e4x+15e8x5x2+(240120e415e8+5x)log(5)+(5x2+(240120e415e8)log(5))log(x)log(log(x))(2304x2+144e12x2+9e16x296x3+x4+e4(2304x248x3)+e8(864x26x3)+(4608x288e12x18e16x+192x22x3+e8(1728x+12x2)+e4(4608x+96x2))log(5)+(2304+144e12+9e16+e4(230448x)+e8(8646x)96x+x2)log2(5))log(x)dx
  3.14.21 3xx2+(x+2x2)log(x)e1+e4+e1+e4xxxlog2(x)xlog2(x)dx
  3.14.22 4010xe8x+e4(30x10x2)+(30x2e4x10x2)log(x)xlog2(x)3e8x+e4(120x+30x2)+(120x+6e4x+30x2)log(x)+3xlog2(x)dx
  3.14.23 2x7x29x3+27x49x5+e3(6x26x3)+(2+6e3x+9x3)log(x)9x49x5+9x3log(x)dx
  3.14.24 15+15x+2x2+6x3+x75x8+3x9+(4x73x8)log(x)5x2x3x9+x8log(x)dx
  3.14.25 e2(1+iπ+log(3+2log(5)))x(22(iπ+log(3+2log(5))))x2dx
  3.14.26 2exx+2x3+e(ex+x2)x+log(x)x(ex+x2)x+log(x)x(exx2+2x3+(exx+2x2)log(x)+(ex+x2+(exx2)log(x))log(ex+x2))exx2x4+e(ex+x2)x+log(x)x(exx2+x4)+(exx2+x4)log(x2)dx
  3.14.27 (e2e2xlog2(2x)(10e10+40e10+2xlog(2x)40e10+2xxlog2(2x))+e4e2xlog2(2x)(2e20x8e20+2xxlog(2x)+8e20+2xx2log2(2x)))dx
  3.14.28 20+360x270x2+15xlog(x)18x2+xlog(x)dx
  3.14.29 e2+x(12x+x2)+e5+4xx2+x31+x(12x+x2)+(e2+x(x2x2+x3)+e5+4xx2+x31+x(x+2x24x3+2x4))log(x)(e2+x(x2x2+x3)+e5+4xx2+x31+x(x2x2+x3))log(x)dx
  3.14.30 116e168xx2(15e16+8x+x2+40x160x240x3)dx
  3.14.31 100+40x+4x2+(5040x6x2)log(x)+(10x+2x2)log2(x)4xlog3(x)+(4+2x)log4(x)+2log5(x)+((10020x)log(x)20log3(x))log(2+log(x))+(20040x+(100+40x)log(x)10xlog2(x))log2(2+log(x))+100log(x)log3(2+log(x))+(10050log(x))log4(2+log(x))2xlog3(x)+xlog4(x)dx
  3.14.32 16+8x+2x42x5+(16+16x316x4)log(x)+(32x232x3)log2(x)x4+8x3log(x)+16x2log2(x)dx
  3.14.33 729+27x972x3+270x628x9+x12+e(812187x2+729x581x8+3x11)+(729891x3+171x69x9+e(2187x2+486x527x8))log(13(3e+x))+(243270x3+27x6+e(729x2+81x5))log2(13(3e+x))+(2781ex227x3)log3(13(3e+x))81e+27xdx
  3.14.34 13225x2+e10+4xx2+x4+e5+2xx(24+2x2x2)14424x2+e10+4xx2+x4+e5+2xx(242x2)dx
  3.14.35 2x24x3+e(82x2)+ex(e(4x)+x22x3)+(2e+e1+x)log(2+ex)2x2+exx2dx
  3.14.36 e2x(6x52x6+ex(6x26x3+2x4+10e2+xx4+12x52x6)+e2x(2+2x6x28x3+6x5+e4+2x(4x3+2x4)+e2+x(4x8x22x3+10x4+2x5)))dx
  3.14.37 14x16x24x3+e2x(2exx)(2ex+x)2+ex(2832x8x2)+ex(1+7x+4x2+ex(16+8x))2ex+x16x+16x2+4x3+e2x2ex+x+ex(ex(168x)8x4x2)2ex+x+ex(32+32x+8x2)dx
  3.14.38 172(288x+432x2+e4x(1+4x)+(288576x)log(x)+144log2(x))dx
  3.14.39 ee+ee+x+x2xe2ee+x+2eee+xx2+x4dx
  3.14.40 162x+ee(20x20x2+5x3)(x2+e(20x3+40x415x5))6561+162ee(20x20x2+5x3)x+e2e(20x20x2+5x3)x2dx
  3.14.41 ee5x2ee5xx3dx
  3.14.42 1960+336x+12x2196+28x+x2dx
  3.14.43 1128e2x(xlog(x)+(xx2)log2(x))dx
  3.14.44 1+3x+x2xlog(x)4x+5exxx2+xlog(x)dx
  3.14.45 2+2x+2x26x3+4x2log(4)+(x3x3+2x2log(4))log(x2)+(4x2+2x2log(x2))log(2+log(x2))2x22x4+2x3log(4)+(x2x4+x3log(4))log(x2)+(2x+2x3+(x+x3)log(x2))log(2+log(x2))dx
  3.14.46 15+12e5+x24x16+4e5+x5x4x2dx
  3.14.47 18(16+3x2+e2/x(8+8x))dx
  3.14.48 15e4ex+540e4x+15e2eex5+4x+e2ex(60e2x+120e3x)+eeex5(180e4x30e2ex+2x12eex+5x)5e4exx2+5e2eex5+4xx2+e2ex+2x(40x+60x2)+e4x(80240x+180x2)+eeex5(10e2ex+2xx2+e4x(40x60x2))dx
  3.14.49 5exdx
  3.14.50 1215000+1761750x2972000x4+256320x632256x8+1536x10+e4x(120x496x518x6+24x7)+(1296000+1814400x2977400x4+254112x631872x8+1536x10)log(2)+(518400+699840x2367920x4+94356x611808x8+576x10)log2(2)+(92160+119808x261440x4+15552x61944x8+96x10)log3(2)+(6144+7680x23840x4+960x6120x8+6x10)log4(2)+e3x(5760x3+4320x4864x52232x6192x7+288x8+(1536x3+1152x4192x5576x648x7+72x8)log(2))+e2x(97200x264800x3+45900x4+50760x53168x613248x7576x8+1152x9+(51840x234560x3+23040x4+26496x51368x66768x7288x8+576x9)log(2)+(6912x24608x3+2880x4+3456x5144x6864x736x8+72x9)log2(2))+ex(648000x+324000x2550800x3340200x4+155520x5+133920x614592x723424x8+1536x10+(518400x+259200x2423360x3267840x4+114912x5+103752x610368x717856x8+1152x10)log(2)+(138240x+69120x2108288x370272x4+28224x5+26784x62448x74536x8+288x10)log2(2)+(12288x+6144x29216x36144x4+2304x5+2304x6192x7384x8+24x10)log3(2))1024+1280x2640x4+160x620x8+x10dx
  3.14.51 e4(15618x)8x+e2(104+24x)e4dx
  3.14.52 ((2x)log(4)log(4)log(exx2))dx
  3.14.53 2x3+e.32/x(3+2x)log(2)log2(log(4))2x3dx
  3.14.54 (e5+x2+20x6)log(4)+e4xlog(4)(16x3+4x2log(4))+e3xlog(4)(48x432x3log(4))+e2xlog(4)(48x5+72x4log(4))+exlog(4)(16x664x5log(4))4e4xlog(4)x3log(4)16e3xlog(4)x4log(4)+24e2xlog(4)x5log(4)16exlog(4)x6log(4)+(e5x+x3+4x7)log(4)dx
  3.14.55 (25165824524288x2)log4(4)524288x2log4(4)log(x)+(452984832x+18874368x3196608x5)log3(4)log2(x)+(75497472x+6291456x3163840x5)log3(4)log3(x)+(2717908992x2169869312x4+3538944x624576x8)log2(4)log4(x)+(1358954496x2+28311552x4+589824x612288x8)log2(4)log5(x)+(5435817984x3+452984832x514155776x7+196608x91024x11)log(4)log6(x)+(8153726976x3566231040x5+14155776x7147456x9+512x11)log(4)log7(x)+(16307453952x4+1698693120x670778880x8+1474560x1015360x12+64x14)log9(x)(254803968x+26542080x31105920x5+23040x7240x9+x11)log9(x)dx
  3.14.56 1512x325x2+10x5+x8+(10x+2x4)log(5)+log2(5)dx
  3.14.57 36288x128x2+82x3+56x4+8x5+e156x3+5x+2x2(930x+13x2+20x3+4x4)+e156x3+5x+2x2(1851x4x2+53x3+28x4+4x5)log(x)18x60x2+26x3+40x4+8x5+e156x3+5x+2x2(9x30x2+13x3+20x4+4x5)log(x)dx
  3.14.58 24e402x+x2+e20x(8x+2x2)32e402x16e20xx+2x2dx
  3.14.59 4x(4x2+x2log(7)+log(x)x2)x(12log(x)+(4x2+x2log(7)+log(x))log(4x2+x2log(7)+log(x)4x2))4x2+x2log(7)+log(x)dx
  3.14.60 27x227x345x417x52x6+e6(x22x3)+e4(9x215x36x4)+e2(27x236x333x46x5)+e12515e4+e2(9030x)90x15x29x+e4x+6x2+x3+e2(6x+2x2)(375+15e6+375x+135x2+15x3+e4(135+45x)+e2(395+270x+45x2))27x2+e6x2+27x3+9x4+x5+e4(9x2+3x3)+e2(27x2+18x3+3x4)dx
  3.14.61 8+8x+6x2+7x3+x4+(810x+16x2+2x3)log(4+9x+x215x+5e5x)4x25x3+8x4+x5dx
  3.14.62 4x+8x2+(8+8x)log(5x)+(44x+4x2log(25)+8xlog(5x)+4log2(5x))log(14(44x+4x2log(25)+8xlog(5x)+4log2(5x)))44x+4x2log(25)+8xlog(5x)+4log2(5x)dx
  3.14.63 (164e8+8e232e2x+2x+4x3+e4+4e216e2x(4x+64e2xx2))dx
  3.14.64 13e13(3x+24x24eexx2+3log(54))(12+192x+eex(32x16exx2))dx
  3.14.65 4+6x+(4+9x)log(x)(2x+3x2)log(x)dx
  3.14.66 8x2+e4(6432x+4x2)4x4+e8(25632x2+x4)+e4(64x2+4x4)dx
  3.14.67 96x+24x2+ex2(96+24x)+(32x+16x2+ex2(8x64x2+16x3))log(1x3)16x38x4+x5+e2x2(16x8x2+x3)+ex2(32x216x3+2x4)dx
  3.14.68 150ee2x+150ee2xx2(5+50ee2+xlog(log(4)x)x2)(1050ee2+xx25x)xdx
  3.14.69 25000e25+3x5+x315000e25+3x5+xlog(2+e25+3x5+x)+1318000e25+3x5+xlog2(2+e25+3x5+x)1831200e25+3x5+xlog3(2+e25+3x5+x)(50+20x+2x2+e25+3x5+x(25+10x+x2))log5(2+e25+3x5+x)dx
  3.14.70 56x2+62x4+28x5+10x6+4x7+e5(1428x2x24x3)+(112x2168x372x424x58x6)log(5)+(56+112x+106x2+44x3+14x4+4x5)log2(5)+(56x2+48x3+22x4+18x5+6x6+e5(142x6x2)+(112x112x260x340x412x5)log(5)+(56+64x+38x2+22x3+6x4)log2(5))log(5xe5+4x2+4x3+x4+(8x8x22x3)log(5)+(4+4x+x2)log2(5))+(2e5x+8x3+8x4+2x5+(16x216x34x4)log(5)+(8x+8x2+2x3)log2(5))log2(5xe5+4x2+4x3+x4+(8x8x22x3)log(5)+(4+4x+x2)log2(5))e5+4x2+4x3+x4+(8x8x22x3)log(5)+(4+4x+x2)log2(5)dx
  3.14.71 1125ex+x2(810x+17x22x3)dx
  3.14.72 8x2+2x3+3x4x5+(2x)log(5)+(8x2+4x3+9x44x52log(5))log(x)x2dx
  3.14.73 11+e2xx2+ex(2x+10x2)+(11+12exxe2xx2)log(44x+4exx21+exx)log(log(44x+4exx21+exx))(55x260exx3+5e2xx4)log(44x+4exx21+exx)+(110x+120exx210e2xx3)log(44x+4exx21+exx)log(log(44x+4exx21+exx))+(5560exx+5e2xx2)log(44x+4exx21+exx)log2(log(44x+4exx21+exx))dx
  3.14.74 x2+e5+x(4+x2)+(44e5+xx3)log(x)+(e5+xx2+(x2+e5+xx2)log(x))log(e5x(e5+x+(1+e5+x)log(x)))e5+xx2+(x2+e5+xx2)log(x)dx
  3.14.75 e8+ee4x6+e4(2500x3200x6+36x7+4x9)+e8(39062562500x3+11250x4+3750x6900x7+81x8100x9+18x10+x12)e8x8+e4x6+e4(2500x3200x6+36x7+4x9)+e8(39062562500x3+11250x4+3750x6900x7+81x8100x9+18x10+x12)e8x8+4x6+e4(2500x3200x6+36x7+4x9)+e8(39062562500x3+11250x4+3750x6900x7+81x8100x9+18x10+x12)e8x8(8x6+e4(12500x3+400x636x7+4x9)+e8(3125000+312500x345000x47500x6+900x7100x9+36x10+4x12))x9dx
  3.14.76 6x5log2(20+e24)dx
  3.14.77 x2+e48+12x212x3+e5(36x2+12x3)x(48+12x224x3+e5(36x2+24x3))x2dx
  3.14.78 10+12x6x2+e20+x(6+12x6x2)+(9+23x17x2+3x3+e20+x(36x+3x2))log(3672x+36x281252x+250x284x3+9x4+e40+2x(918x+9x2)+e20+x(54+138x102x2+18x3))(9+23x17x2+3x3+e20+x(36x+3x2))log(3672x+36x281252x+250x284x3+9x4+e40+2x(918x+9x2)+e20+x(54+138x102x2+18x3))dx
  3.14.79 e1x+(15+9x3log(4)+ex(53x+log(4)))log(x)(15+8x3log(4)+ex(53x+log(4))+(9x+ex(2x3x2+xlog(4)))log(x))x3+(30x218x3+6x2log(4)+ex(10x2+6x32x2log(4)))log(x)+(225x270x2+81x3+(90x54x2)log(4)+9xlog2(4)+ex(150x+180x254x3+(60x+36x2)log(4)6xlog2(4))+e2x(25x30x2+9x3+(10x6x2)log(4)+xlog2(4)))log2(x)dx
  3.14.80 eeex(ex(3x)+x)x(eex(ex(3x)+x)(4x24exx24x3)+eeex(ex(3x)+x)(e2x(1+x)+ex(4x2)))x2dx
  3.14.81 12e10xdx
  3.14.82 e2(189x+198x2+111x3+30x4+3x5+e8(432x+288x2+48x3)+e4(216x+432x2+192x3+24x4))9+6x+x2(1134+1998x+1998x2+942x3+210x4+18x5+e8(2592+2592x+864x2+96x3)+e4(1296+4752x+3456x2+960x3+96x4))27+27x+9x2+x3dx
  3.14.83 33x5x2+3x3+2x4+(3+6x+3x2+6x3+6x4)log(4x1+x2)54x2108x3+36x436x5+6x6+72x7+24x8dx
  3.14.84 e29x2+6x3+x4(128x)+54x4108x536x6+56x7+30x8+4x9+e19x2+6x3+x4(12x4x262x3+54x4+90x5+34x6+4x7)27x3+27x4+9x5+x6dx
  3.14.85 4+(4x)log(4x)+(8x+6x22x3)log(x)+(4x2x3)log2(x)8x2+2x3dx
  3.14.86 7x2+4ee1+4xx2x+1+4xx2x(22x2)x2dx
  3.14.87 (6416x)log(x)+(64x+16x2)log(x)log(2x)+(6416x+(6448x)log(x))log(2x)log(exlog(2x))(64x2+48x312x4+x5)log2(x)log(2x)dx
  3.14.88 5ex+5x220x3+20x4+(8x216x3)log(x)+3x2log2(x)1255ex+x34x4+4x5+(2x34x4)log(x)+x3log2(x)dx
  3.14.89 ex(25+10x+21x2+4x3+4x4)+ee3+5x+x2+2x35+x+2x2(25+e3(14x)+10x+21x2+4x3+4x4)25+10x+21x2+4x3+4x4dx
  3.14.90 18753e+e2x(12522e4x)390625+e22500x+4x2+e(1250+4x)dx
  3.14.91 15(1+15x2)dx
  3.14.92 e14(154ex+20x5log(3))(exxlog(4)+(1+5x)log(4))x2dx
  3.14.93 118x+2e2x3x21x9x2+e2x2x3dx
  3.14.94 ee9x(40+10x+e9x(12280x+10x2)+e9x(6140x+5x2)log(6140x+5x2))6140x+5x2dx
  3.14.95 10020x+20x284x3+76x412x5+(20+4x216x3+12x4)log(x)+e2(10+10x)log(5x+log(x))+(e2(255x)+5e2log(x))log2(5x+log(x))20x24x3+4x2log(x)dx
  3.14.96 279x39x2+(2+7x+6x2)log(x)+(6x+3x2)log(2x+x2)8x2+4x3+(16x+632x2+312x3)log(x)+(8+628x+12480x2+6084x3)log2(x)+((48x224x3)log(x)+(48x1896x2936x3)log2(x))log(2x+x2)+(72x2+36x3)log2(x)log2(2x+x2)dx
  3.14.97 ee2xx2(9+ex(4818x)x+e2x(61+48x+9x2)x2)(1818x+ex(48+12x+18x2)x+e2x(48x+18x2)x2)2e2xx+e2x+e2xx2(9+ex(4818x)x+e2x(61+48x+9x2)x2)xdx
  3.14.98 (2ex2x+22x2e50x(2+2e50)log(2))dx
  3.14.99 e16+10x2x2(7x)(69+38x4x2)+ex(76x+x2)63+9xdx
  3.14.100 68x468x5+17x6+e2x2+2x3(6868x+17x2)+ex2+x(128x+160x232x3)+ex2+x3(136x2+136x334x4+ex2+x(32128x+320x2224x3+48x4))64x464x5+16x6+e2x2+2x3(6464x+16x2)+ex2+x3(128x2+128x332x4)dx