해법
∫(x+4)14dx
해법
15x15+4x14+112x13+35824x12+23296x11+51025024x10+34100096x9+7028736x8+28114944x7+3262406144x6+51049624576x5+381681664x4+31526726656x3+469762048x2+268435456x+C
솔루션 단계
∫(x+4)14dx
(x+4)14확대한다:x14+56x13+1456x12+23296x11+256256x10+2050048x9+12300288x8+56229888x7+196804608x6+524812288x5+1049624576x4+1526726656x3+1526726656x2+939524096x+268435456
=∫x14+56x13+1456x12+23296x11+256256x10+2050048x9+12300288x8+56229888x7+196804608x6+524812288x5+1049624576x4+1526726656x3+1526726656x2+939524096x+268435456dx
합계 규칙 적용: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx=∫x14dx+∫56x13dx+∫1456x12dx+∫23296x11dx+∫256256x10dx+∫2050048x9dx+∫12300288x8dx+∫56229888x7dx+∫196804608x6dx+∫524812288x5dx+∫1049624576x4dx+∫1526726656x3dx+∫1526726656x2dx+∫939524096xdx+∫268435456dx
∫x14dx=15x15
∫56x13dx=4x14
∫1456x12dx=112x13
∫23296x11dx=35824x12
∫256256x10dx=23296x11
∫2050048x9dx=51025024x10
∫12300288x8dx=34100096x9
∫56229888x7dx=7028736x8
∫196804608x6dx=28114944x7
∫524812288x5dx=3262406144x6
∫1049624576x4dx=51049624576x5
∫1526726656x3dx=381681664x4
∫1526726656x2dx=31526726656x3
∫939524096xdx=469762048x2
∫268435456dx=268435456x
=15x15+4x14+112x13+35824x12+23296x11+51025024x10+34100096x9+7028736x8+28114944x7+3262406144x6+51049624576x5+381681664x4+31526726656x3+469762048x2+268435456x
솔루션에 상수 추가=15x15+4x14+112x13+35824x12+23296x11+51025024x10+34100096x9+7028736x8+28114944x7+3262406144x6+51049624576x5+381681664x4+31526726656x3+469762048x2+268435456x+C