$\int$ (1-x⁸)^-1 dx

gokusuper

$\int$ (1-x⁸)^-1 dx

mukundmadhav

Split as 1/2[ 1/(1-x^4) + 1/(1+x^4)]
Now Split the first term into 1/2[1/(1-x^2) + 1/(1+x^2)]
You can integrate the second term by splitting it as (x^2+i)(x^2-i)
Then use the same method as you would for x^2 + a^2.. where a=root(i)
The final answer comes out to b e real.. It's too complicated for me to do and I'm not comfortable with the equation sytem of goiit.. try to figure it out.. Nahi hota to tell me..

couda.draconis

Full credits to mukund madhav for the correct reasoning :: The correct answer (for reference )

is available at the http://integrals.wolfram.com/index.jsp

Just type in ur integral and pronto:

Btw urs took only 0.06 s to compute

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$\int$ (1-x⁸)^-1 dx