Plz answer this question guys...

1.	Plz answer this question guys...
Answer» ong>GIVEN : $\displaystyle{\sf \int \dfrac{x^2+1}{x^4+1} \:dx}$ SOLUTION : $\displaystyle{\sf \implies \int \dfrac{x^2+1}{x^4+1} \:dx}\\$ $\displaystyle{\sf \implies \int \dfrac{\Big(1+\dfrac{1}{x^2}\Big)}{\Big(x^2+\dfrac{1}{x^2}\Big)} \:dx}\\$ $\displaystyle{\sf \implies \int \dfrac{1+\dfrac{1}{x^2}}{2-2+x^2+\dfrac{1}{x^2}}}\\$ Using Substitution, $\boxed{\sf x-\dfrac{1}{x}=t \Rightarrow 1+\dfrac{1}{x^2}\:dx=dt}$ $\displaystyle{\sf \implies \int \dfrac{1}{t^2+2}\:dt}\\$ $\displaystyle{\sf \implies \dfrac{1}{\sqrt{2}}\:tan^{-1}\Big(\dfrac{t}{\sqrt{2}}\Big)+C}\\$ $\displaystyle{\implies \sf \dfrac{1}{\sqrt{2}} \:tan^{-1}\bigg(\dfrac{x^2-1}{\sqrt{2}x}\bigg)+C}$ Required Answer : $\boxed{\boxed{\displaystyle{\sf \int \dfrac{x^2+1}{x^4+1}\:dx = \dfrac{1}{\sqrt{2}}\:tan^{-1}\bigg(\dfrac{x^2-1}{\sqrt{2}x}\bigg) +C}}}$

Answer»

ong>GIVEN :

$\displaystyle{\sf \int \dfrac{x^2+1}{x^4+1} \:dx}$