`int((x^(2)+1))/((x^(4)+1))dx=?`A. `(1)/(sqrt(2))tan^(-1)(x-(1)/(x))+C`B. `(1)/(sqrt(2))cot^(-1){(x-(1)/(x))}+C`C. `(1)/(sqrt(2))tan^(-1){(1)/(sqrt(2))(x-(1)/(x))}+C`D. none of these

`int((x^(2)+1))/((x^(4)+1))dx=?`A. `(1)/(sqrt(2))tan^(-1)(x-(1)/(x))+C

1.	`int((x^(2)+1))/((x^(4)+1))dx=?`A. `(1)/(sqrt(2))tan^(-1)(x-(1)/(x))+C`B. `(1)/(sqrt(2))cot^(-1){(x-(1)/(x))}+C`C. `(1)/(sqrt(2))tan^(-1){(1)/(sqrt(2))(x-(1)/(x))}+C`D. none of these
Answer» Correct Answer - C On dividing the numerator and denominator by `x^(2)`, we get `I=int((1+(1)/(x^(2))))/((x^(2)+(1)/(x^(2))))dx=int((1+(1)/(x^(2))))/({(x-(1)/(x))^(2)+2})dx` `=int(dt)/((t^(2)+2))," where "(x-(1)/(x))=t and(1+(1)/(x^(2)))dx=dt` `int(dt)/([t^(2)+(sqrt(2))^(2)])=(1)/(sqrt(2))+C=(1)/(sqrt(2))tan^(-1){(1)/(sqrt(2))(x-(1)/(x))}+C`.