`int 1/ (x^2 + a^2) dx = 1/a tan^-1 (x/a) + c`

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

If int (dx)/((x^(2)+a^(2))^(2))=(1)/(ka^(2)){(x)/(x^(2)+a^(2))+(1)/(a) tan^(-1). (x)/(a)}+C . Then the value of k, is

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

Prove that int e^x (tan^-1 x+1/(1+x^2)) dx=e^x tan^-1x+c

int_0^1 tan^1x/(1+x^2)dx

2int_ (0) ^ ((1) / (sqrt (2))) (sin ^ (- 1) x) / (x) dx-int_ (0) ^ (1) (tan ^ (- 1) x) / (x) dx =

" 1.If "int(1)/((x^(2)+1)(x^(2)+4))dx=G tan^(-1)x+H tan^(-1)((x)/(2))+C,C in A." Then "G=.......,H=...?