निम्न फलनों का समाकलन कीजिये - `(x^(8))/((1-x^(3))^(1/3))`

निम्न फलनों का समाकलन कीजि

1.	निम्न फलनों का समाकलन कीजिये - `(x^(8))/((1-x^(3))^(1/3))`
Answer» माना `I = int (x^(8))/((1-x^(3))^(1//3))dx` माना `1 -x^(3) = t rArr - 3x^(2)dx = dt` `rArr " " x^(2) dx = - (1)/(3)dt` तथा ` 1- x^(3) = t rArr 1 - t = x^(3)` `because" "I = int((x^(3))^(2)x^(2)dx)/((1-x^(3))^(1//3)) = - (1)/(3)int((1-t)^(2)dt)/(t^(3//2))` ` = - (1)/(3)int((1-2t +t^(2))/(t^(1//3)))dt` `= - (1)/(3)int(t^(-1//3) - 2t^(2//3) + t^(5//3))dt` ` =- (1)/(3)[(3)/(2)t^(2//3) -(6)/(5)t^(5//3) + (3)/(8)t^(8//3)]` `= - (1)/(3)[(3)/(2)(1-x^(3))^(2//3)- (6)/(5)(1-x^(3))^(5//3) + (3)/(8)(1-x^(3))^(8//3)]`