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# Can ny1 plzz tel the integration of x4+1/x6+1..??? fast...

Aman Bansal
592 Points
8 years ago

Dear Ranjita,

The integration gives: x5/5 + ln((x^7)/(7) + lx)

1/(x^6+1) = (1/3)(1/(x^2+1)) + (2/3-x^2/3)/(x^4-x^2+1).

The next step is to factor

x^4-x^2+1 = (x^2-sqrt(3) x +1)(x^2+sqrt(3)+1)

and do partial fractions on

1/(x^4-x^2+1)

Sorry about that square root of three.

PS. A clever way to see the factorization is to write

x^4-x^2+1= (x^2+1)^2-3x^2

which is a difference of squares that is easily factored.

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Aman Bansal