[int tan^(-1)sqrt(x)dx=?],[(a)(x-1)tan^(-1)sqrt(x)+sqrt(x)+C,(b)(x+1)tan^(-1)sqrt(x)-sqrt(x)+C],[(c)(1)/(2)sqrt(x)tan^(-1)sqrt(x)-(1)/(2)sqrt(x)+C,(d)" none of these "]

if int tan^(-1)sqrt(x)dx=u tan^(-1)sqrt(x)-sqrt(x)+c then u=

tan^(-1)((sqrt(1+x)+sqrt(1-x))/(sqrt(1+x)-sqrt(1-x)))

tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))

tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))

int(x+2)/((x^(2)+3x+3)sqrt(x+1))dx is equal to a) (1)/(sqrt(3))tan^(-1)((x)/(sqrt(3)(x+1))) b) (2)/(sqrt(3))tan^(-1)((x)/(sqrt(3(x+1)))) c) (2)/(sqrt(3))tan^(-1)((x)/(sqrt(x+1))) d)None of these

tan^-1 (sqrt(x)+sqrt(a))/(1-sqrt(x)sqrt(a))

y=tan^(-1)((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)))

int sqrt((x)/(1-x))dx is equal to sin^(-1)sqrt(x)+C(b)sin^(-1){sqrt(x)-sqrt(x(1-x))}+C(c)sin^(-1){sqrt(x(1-x)}+C(d))sin^(-1)sqrt(x)-sqrt(x(1-x))+C

int (dx)/(sqrt(1+sqrt(x)))=(4)/(3)(sqrt(x)-2)sqrt(1+sqrt(x))+c