If `l=int(x^(5))/(sqrt(1+x^(3)))dx`, then l is equal to

Options

A. `(2)/(9)(1+x^(3))^((5)/(2))+(2)/(3)(1+x^(3))^((3)/(2))+C`
B. `log|sqrtx+sqrt(1+x^(3))|+C`
C. `log|sqrtx-sqrt(1+x^(3))|+C`
D. `(2)/(9)(1+x^(3))^((3)/(2))-(2)/(3)(1+x^(3))^((1)/(2))+C`

Answer

D

Explanation

Given, `" "l=int(x^(5))/(sqrt(1+x^(3)))dx`
Let`" "1+x^(3)=t`
`rArr" "3x^(2)dx=dt`
`therefore" "l=int((t-1))/(sqrtt).(dt)/(3)=(1)/(3)int(sqrtt-t^(-1//2))dt`
`=(1)/(3)[(2t^(3//2))/(3)-2t^(1//2)]+c`
`=(2)/(9)(1+x^(3))^(3//2)-(2)/(3)(1+x^(3))^(1//2)+C`