# Answer to Question #5668 in Calculus for drew callahan

Question #5668

Integrate 12x^3(6x^4-1)^5dx

Expert's answer

Integrate 12x^3(6x^4-1)^5dx.

12x^3(6x^4-1)^5 = 12x^3(7776x^20 - 6480x^16 + 2160x^12 - 360x^8 + 30x^4 - 1) =

& = 93312x^23 - 77760x^19 + 25920x^15 - 4320x^11 + 360x^7 - 12x^3

int(93312x^23 - 77760x^19 + 25920x^15 - 4320x^11 + 360x^7 - 12x^3)dx =

& = int(93312x^23)dx - int(77760x^19)dx + int(25920x^15)dx - int(4320x^11)dx + int(360x^7)dx - int(12x^3)dx =

& = 93312*int(x^23)dx - 77760*int(x^19)dx + 25920*int(x^15)dx - 4320*int(x^11)dx + 360*int(x^7)dx - 12*int(x^3)dx =

& = 93312*1/21*x^21 - 77760*1/20*x^20 + 25920*1/16*x^16 - 4320*1/12*x^12 + 360*1/8*x^8 - 12*1/4*x^4 =

& = 31104/7*x^21 - 3888*x^20 + 1620*x^16 - 360*x^12 + 45*x^8 - 3*x^4.

12x^3(6x^4-1)^5 = 12x^3(7776x^20 - 6480x^16 + 2160x^12 - 360x^8 + 30x^4 - 1) =

& = 93312x^23 - 77760x^19 + 25920x^15 - 4320x^11 + 360x^7 - 12x^3

int(93312x^23 - 77760x^19 + 25920x^15 - 4320x^11 + 360x^7 - 12x^3)dx =

& = int(93312x^23)dx - int(77760x^19)dx + int(25920x^15)dx - int(4320x^11)dx + int(360x^7)dx - int(12x^3)dx =

& = 93312*int(x^23)dx - 77760*int(x^19)dx + 25920*int(x^15)dx - 4320*int(x^11)dx + 360*int(x^7)dx - 12*int(x^3)dx =

& = 93312*1/21*x^21 - 77760*1/20*x^20 + 25920*1/16*x^16 - 4320*1/12*x^12 + 360*1/8*x^8 - 12*1/4*x^4 =

& = 31104/7*x^21 - 3888*x^20 + 1620*x^16 - 360*x^12 + 45*x^8 - 3*x^4.

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