`IfI=int(dx)/((2a x+x^2)^(3/2))`,then `I` is equal to`` (a)`-(x+a)/(sqrt(2a x+x^2))+c` (b) `-1/a(x+a)/(sqrt(2a x+x^2))+c` (c)`-1/(a^2)(x+a)/(sqrt(2a x+x^2))+c` (d) `-1/(a^3)(x+a)/(sqrt(2a x+x^3))+c`

If int(x)/(sqrt(8-2x-x^(2)))dx=a sin^(-1)((x+1)/(3))+b sqrt(8-2x-x^(2))+c , then

If tan^(-1)x+2cot^(-1)x=(2 pi)/(3), then x, is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3)(d)sqrt(2)

int(dx)/(sqrt(a^(2)-x^(2)))=sin^(-1)(x/a)+C

int(1)/(sqrt(sin^(3)x cos x))dx is equal to :(A)-(2)/(sqrt(cos x))+c(B)(2)/(sqrt(tan x))+c(C)(2)/(sqrt(cot x))+c(D)(2)/(sqrt(tan x))+c

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

Show that int(1)/(x^(2)sqrt(a^(2)+x^(2)))dx=(-1)/(a^(2))(sqrt(a^(2)+x^(2)))/(x)+c

IfI=int(dx)/(x^(3)sqrt(x^(2)-1)), then Iequals a.(1)/(2)((sqrt(x^(2)-1))/(x^(3))+tan^(-1)sqrt(x^(2)-1))+C b.(1)/(2)((sqrt(x^(2)-1))/(x^(2))+x tan^(-1)sqrt(x^(2)-1))+Cc(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+Cd(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+C

d/(dx)(sin^(-1)x+cos^(-1)x) is equal to : (A) (1)/(sqrt(1-x^(2))), (B) (2)/(sqrt(1-x^(2))), (C) 0 (D) sqrt(1-x^(2))

int(x^(3)dx)/(sqrt(1+x^(2))) is equal to (A) (1)/(3)sqrt(1+x^(2))(2+x^(2))+C(B)(1)/(3)sqrt(1+x^(2))(x^(2)-1)+C(C)(1)/(3)(1+x^(2))^((3)/(2))+C(D)(1)/(3)sqrt(1+x^(2))(x^(2)-2)+C

int(x^((3)/(2))+(1)/(sqrt(x)))dx is equal to (2)/(5)x^((5)/(2))+2sqrt(x)+c (b) (5)/(2)x^((5)/(2))+2sqrt(x)+c(2)/(5)x^((5)/(2))-2sqrt(x)+c(d)(1)/(2)x^((3)/(2))+2sqrt(x)+c