`"If "int x^(5)(1+x^(3))^(2//3)dx=A(1+x^(3))^(8//3)+B(1+x^(3))^(5//3)+c, " then " `A. `A=(1)/(4),B=(1)/(5)`B. `A=(1)/(8),B=-(1)/(5)`C. `A=-(1)/(8),B=(1)/(5)`D. non of these

`"If "int x^(5)(1+x^(3))^(2//3)dx=A(1+x^(3))^(8//3)+B(1+x^(3))^(5//3)+

1.	`"If "int x^(5)(1+x^(3))^(2//3)dx=A(1+x^(3))^(8//3)+B(1+x^(3))^(5//3)+c, " then " `A. `A=(1)/(4),B=(1)/(5)`B. `A=(1)/(8),B=-(1)/(5)`C. `A=-(1)/(8),B=(1)/(5)`D. non of these
Answer» Correct Answer - B `"Here, " int x^(5)(1+x^(3))^(2//3)dx` `"Let " 1+x^(3)=t^(2) " and " 3x^(2)dx=2tdt ` `:. int x^(5)(1+x^(3))^(2//3)dx =int x^(3)(1+x^(3))^(2//3)x^(2)dx ` `=int(t^(2)-1)(t^(2))^(2//3)x^(2)dx ` `=(2)/(3)int(t^(2)-1)t^(7//3)dt` `=(2)/(3)int(t^(13//3)-t^(7//3))dt ` `=(2)/(3){(3)/(16)t^(16//3)-(3)/(10)t^(10//3)}+C ` `=(1)/(8)(1+x^(3))^(8//3)-(1)/(5)(1+x^(3))^(5//3)+C`

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