`int(dx)/((1+sqrt(x))sqrt((x-x^2)))i se q u a lto` (a)`(1+sqrt(x))/((1-x)^2)+c` (b) `(1+sqrt(x))/((1+x)^2)+c` (c)`(1-sqrt(x))/((1-x)^2)+c` (d) `(2(sqrt(x)-1))/(sqrt((1-x)))+c`

(i)int(1)/(sqrt(x+1)+sqrt(x+2))dx

-int(1)/(sqrt(1-x)+sqrt(1+x))(-(1)/(2sqrt(1-x))+(1)/(2sqrt(1+x)))xdx

int_(-1)^(1) (sqrt(1+x+x^(2))-sqrt(1-x+x^(2))) dx =

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

(d)/(dx)[cos^(-1)(x sqrt(x)-sqrt((1-x)(1-x^(2))))]=(1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(-1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))+(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))0 b.1/4c.-1/4d none of these

tan(cos^(-1)x) is equal to (x)/(1+x^(2)) b.(sqrt(1+x^(2)))/(x) c.(sqrt(1-x^(2)))/(x) d.sqrt(1-2x)

If int(x)/(sqrt(1+x^(2)+sqrt((1+x^(2))^(3))dx))=k sqrt(1+sqrt(1+x^(2))+c. find k)

int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

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

int_(-1)^(1)(sqrt(1+x+x^(2))-sqrt(1-x+x^(2)))dx=