`int(x^(3)-1)^(1//3)x^(5)dx` is equal toA. `(1)/(7)(x^(3)+1)^(1//3)+(1)/(4)(x^(3)-1)^(3//4)+C`B. `(1)/(7)(x^(3)-1)^(7//3)+(1)/(4)(x^(3)-1)^(4//3)+C`C. `(3)/(7)(x^(3)-1)^(7//3)+(1)/(4)(x^(3)-1)^(4//3)+C`D. None of the above

`int(x^(3)-1)^(1//3)x^(5)dx` is equal toA. `(1)/(7)(x^(3)+1)^(1//3)+(1

1.	`int(x^(3)-1)^(1//3)x^(5)dx` is equal toA. `(1)/(7)(x^(3)+1)^(1//3)+(1)/(4)(x^(3)-1)^(3//4)+C`B. `(1)/(7)(x^(3)-1)^(7//3)+(1)/(4)(x^(3)-1)^(4//3)+C`C. `(3)/(7)(x^(3)-1)^(7//3)+(1)/(4)(x^(3)-1)^(4//3)+C`D. None of the above
Answer» Correct Answer - B `int(x^(3)-1)^(1//3)x^(5)dx=int(x^(3)-1)^(1//3)x^(3).x^(2)dx` Let `x^(3)-1=t rArr x^(3)=t+1` Differentiating w.r.t. x, we get `3x^(2)=(dt)/(dx) rArr dx=(dt)/(3x^(2))` `therefore" "intx^(3)-1^(1//3)x^(3).x^(2)dx=intt^(1//3)(t+1)x^(2)(dt)/(3x^(2))` `=(1)/(3)int(t^(4//3)+t^(1//3))dt` `=(1)/(3)[(t^(7//3))/((7)/(3))+(t^(4//3))/((4)/(3))]+C=(1)/(3)[(3)/(7)t^(7//5)+(3)/(4)t^(4//3)]+C` `=(1)/(7)t^(7//3)+(1)/(4)t^(4//3)+C` `=(1)/(7)(x^(3)-1)^(7//3)+(1)/(4)(x^(3)-1)^(4//3)+C`