`inttan^(-1)(secx+tanx)dx=?`A. `(pix)/(4)+(x^(2))/(4)+C`B. `(pix)/(4)-(x^(2))/(4)+C`C. `(1)/((1+x^(2)))+C`D. none of these

`inttan^(-1)(secx+tanx)dx=?`A. `(pix)/(4)+(x^(2))/(4)+C`B. `(pix)/(4)-

1.	`inttan^(-1)(secx+tanx)dx=?`A. `(pix)/(4)+(x^(2))/(4)+C`B. `(pix)/(4)-(x^(2))/(4)+C`C. `(1)/((1+x^(2)))+C`D. none of these
Answer» Correct Answer - A `tan^(-1)(secx+tanx)=tan^(-1)((1)/(cosx)+(sinx)/(cosx))=tan^(-1){(1+sinx)/(cosx)}`. `=tan^(-1){(1-cos((pi)/(2)+x))/(sin((pi)/(2)+x))}=tan^(-1){(2sin^(2)((pi)/(4)+(x)/(2)))/(2sin((pi)/(4)+(x)/(2))cos((pi)/(4)+(x)/(2)))}` `=tan^(-1){tan((pi)/(4)+(x)/(2))}=((pi)/(4)+(x)/(2))` `:." "I=int((pi)/(4)+(x)/(2))dx(pix)/(4)+(x^(2))/(4)+C`.