`int(dx)/(sqrt(x+1)+sqrt(x+2)) = (2)/(3)[(x+2)^(3//2)-(x+1)^(3//2)]+c` सिद्ध कीजिये -

`int(dx)/(sqrt(x+1)+sqrt(x+2)) = (2)/(3)[(x+2)^(3//2)-(x+1)^(3//2)]+c`

1.	`int(dx)/(sqrt(x+1)+sqrt(x+2)) = (2)/(3)[(x+2)^(3//2)-(x+1)^(3//2)]+c` सिद्ध कीजिये -
Answer» बाया पक्ष ` = int(dx)/(sqrt(x+1)+sqrt(x+2))` `= int(dx)/(sqrt(x+2)+sqrt(x+1))` `= int{(1)/(sqrt(x+2)+sqrt(x+1)).(sqrt(x+2)-sqrt(x+1))/(sqrt(x+2) - sqrt(x+1))}dx` `=int(sqrt(x+2)- sqrt(x+1))/(x+2-x-1)dx` `=int(sqrt(x+2)-sqrt(x+1))/(1)dx` `=int(x+2)^(1//2)dx -int(x+1)^(1//2)dx` ` =(2)/(3)(x+2)^(3//2)- (2)/(3)(x+1)^(3//2)+c` ` = (2)/(3)[(x+2)^(3//2)-(x+1)^(3//2)]+c`= दाया पक्ष