[" C) "sqrt(2)tan^(-1)(sqrt(2)tan x)],[" 2."int(dx)/(sqrt(x)+root(3)(x))=]

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

int(1)/(sqrt(1-tan^(2)x))dx

[" 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(1)/(7+5cos x)dx=(1)/(sqrt(6))tan^(-1)((1)/(sqrt(6))(tan x)/(2))+C(b)(1)/(sqrt(3))tan^(-1)((1)/(sqrt(3))(tan x)/(2))+C(c)(1)/(4)tan^(-1)((tan x)/(2))+C(d)(1)/(7)tan^(-1)((tan x)/(2))+C

int(1)/(sqrt(sec^(2)x+tan^(2)x))dx=

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

Assertion (A) : int(dx)/(x^(2) + 2x + 3) = (1)/(sqrt(2)) tan^(-1)((x+1)/(sqrt(2))) + c Reason (R) : int(dx)/(x^(2) + a^(2)) = (1)/(a) tan^(-1)((x)/(a)) + c

int(1+tan^(2)x)/(sqrt(tan^(2)x+3))

int(sec^(2)x)/(sqrt(1-tan^(2)x))dx=?

int(dx)/((1+x^(2))sqrt(tan^(-1)x+4))