Question

Integrate: x2-1 /x4+x2+1 dx

Answer 1

Answer:

So you want to integrate x2-1 /x4+x2+1 dx

For that we need to understand some basic concepts of Integration first.

Her are some formulas :

∫ 1 dx = x + C.

∫ a dx = ax+ C.

∫ xn dx = ((xn+1)/(n+1))+C ; n≠1.

∫ sin x dx = – cos x + C.

∫ cos x dx = sin x + C.

∫ sec2 dx = tan x + C.

∫ csc2 dx = -cot x + C.

∫ sec x (tan x) dx = sec x + C.

Please find the answer in the picture below.

Answer 2

${\large{\bold{\underline{\green{Formulae\: used:}}}}}$

${\large{\boxed{\red{\sf{∫\frac{1}{x}.dx=ln|x|+c}}}}}$

${\large{\boxed{\red{\sf{\frac{d}{dx}(x^{n})=n.x^{n-1}}}}}}$