" (c) "(1)/(x-sqrt(x))" [NCERT] "

inttan(sin^(-1)x)dx is equal to a) (1)/(sqrt(1-x^(2)))+c b) sqrt(1-x^(2))+c c) (-x)/(sqrt(1-x^(2)))+c d) -sqrt(1-x^(2))+c

Differential coefficient of sec(tan^(-1)x) is (x)/(1+x^(2))( b) x sqrt(1+x^(2))(c)(1)/(sqrt(1+x^(2))) (d) (x)/(sqrt(1+x^(2)))

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) (c) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) (c) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

intsqrt(x/(1-x))\ dx is equal to (a) 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

[" 0.",int sin^(-1)sqrt((x)/(a+x))dx" is equal to "],[," 1) "(x+a)tan^(-1)sqrt((x)/(a))-sqrt(ax)+C],[" 3) "(x+a)cot^(-1)sqrt((x)/(a))-sqrt(ax)+C," 2) "(x+a)tan^(-1)sqrt((x)/(a))+sqrt(ax)+C]

int sqrt((1-x)/(1+x))dx is equal to a) sin^(-1)x + sqrt(1 - x^(2)) + C b) sin^(-1) x - 2 sqrt(1 - x^(2)) + C c) 2 sin^(-1) x - sqrt(1 - x^(2)) + C d) sin^(-1)x - sqrt(1 - x^(2)) + C

int(xdx)/(sqrt((1+x^2)+sqrt((1+x^2)^3)))= (a) 1/2ln(1+sqrt(1+x^2))+c (b) 2sqrt(1+sqrt(1+x^2))+c (c) 2(1+sqrt(1+x^2))+c (d) 4sqrt(1+sqrt(1+x^2))+c