`" If "int(1)/(x^(4)+1)dx=(1)/(2sqrt(2))tan^(-1)((x^(2)-1)/(sqrt(2)x))+A+c" .Then "A" is equal to "`

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

STATEMENT-1 : int(e^(log(1+(1)/(x^(2)))))/(x^(2)+(1)/(x^(2)))dx=(1)/(sqrt(2))tan^(-1).(x^(2)-1)/(sqrt(2)x)+c and STATEMENT-2 : e^(logx) is equal to x if x gt 0 .

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

int(x^(2)-1)/((x^(2)+1)sqrt(x^(4)+1)) dx is equal to -

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(sqrt(x^2+1))/(x^(4))dx" is equal to "

int(x^(2)-1)/(x^(3)sqrt(2x^(4)-2x^(2)+1))dx is equal to

int((x^(2)-1))/((x^(2)+1)sqrt(x^(4)+1))dx is equal to

int((x-1)^(2))/(x^(4)+x^(2)+1)dx=(1)/(sqrt(a))tan^(-1)((x^(2)-1)/(x sqrt(3)))-(b)/(sqrt(a))tan^(-1)((2x^(2)+1)/(3))+ then a^(2)+b^(2) is