`int (x^(8) dx)/((1-x^(3))^(1//3))` का मान ज्ञात कीजिए।

Explanation

माना `1-x^(3) =t`
`:. -3x^(2) dx=dt`
`x^(2) dx=-(dt)/3`
`int (x^(8) dx)/((1-x^(3))^(1//3))=int ((x^(3))^(2) x^(2) dx)/((1-x^(3))^(1//3))`
`=-1/3 int ((1-t)^(2) dt)/t^(1//3)`
`=-1/3 int ((t^(2)-2t+1)dt)/t^(1//3)`
`=-1/3 int (t^(5//3)-2t^(2//3)+t^(-1//3)) dt`
`=-1/3 [t^(8//3)/(8/3)- (2t^(5//3))/(5/3)+ t^(2/3)/(2/3)]+c`
`=-1/3 [3/8 (1-x^(3))^(8//3)-6/5(1-x^(3))^(5//3)+3/2 (1-x^(3))^(2//3)]+c`
`=-1/8 (1-x^(3))^(8//3)+2/5 (1-x^(3))^(5//3)-1/2 (1-x^(3))^(2//3)+c`.