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

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

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

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

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

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

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

int_( then )^( If )(1)/(1-tan^(2)x)dx=f(x)+(1)/(4)ln tan((pi)/(4)+x)+c

If 2int_(0)^(1) tan^(-1)xdx=int_(2)^(1)cot^(-1)(1-x+x^(2))dx . Then int_(0)^(1) tan^(-1)(1-x+x^(2))dx is equal to

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

int(1)/(1+3cos^(2)x)dx=(1)/(2)tan^(-1)((tan x)/(2))+c