`int(x^(2)dx)/(sqrt(x+2))`का माना ज्ञात कीजिये |

`int(x^(2)dx)/(sqrt(x+2))`का माना ज्ञात की�

1.	`int(x^(2)dx)/(sqrt(x+2))`का माना ज्ञात कीजिये \|
Answer» माना ` I = int(x^(2)dx)/(sqrt((x+)))" "....(1)` माना `x + 2 = t rArr x = t - 2` तथा `dx = dt` अतः समी से `I = int((t-2))/((t)^(1//2)) = int ((t^(2) - 4t + 4)/(t^(1//2)))dt` ` = int(t^(3//2) -4t^(1//2) + 4t^(-1//2))dt ` `= (2)/(5)t^(5//2) - (8)/(3)t^(3//2) + 8t^(1//2)` `= (2)/(5)(x+2)^(5//2) - (8)/(3)(x+2)^(3//2)+8(x+2)^(1//2)`