Question

Integrate..

Answer 1

\[\int\limits_{}^{}\frac{ 1 }{ 1-x ^{4} }dx\]

Answer 2

Have you tried partial fractions?

Answer 3

Yeah, we should get it by partial fractions. I was trying to find out another way.

Answer 4

Is this way possible,
\[\frac{ 1 }{ 1-x ^{4} }=\frac{ 1 }{ 2 } (\frac{ 1+x ^{2} }{ 1-x ^{4}}+ \frac{ 1-x ^{2} }{1-x^4 })\]
Now taking out x^2 common for each fraction, using either x-1/x or x+1/x =t as substitution.

Answer 5

What do you mean by "taking out x^2 common for each fraction" ?

Answer 6

No, sorry I just realized that we need a positive sign in denominator like 1+x^4.
Its not possible here.

Answer 7

For example,
\[\frac{ 1-x^2 }{ 1+x^4 } = \frac{ 1-1/x^2 }{ x^2+1/x^2 }\]
Now we can substitute, x+1/x = t and integrate.
This is what I meant @callisto

Answer 8

Got it. I was trying that way only to realize that it didn't work.

Answer 9

Yeah, that is correct @FutureMathProfessor , we were just checking whether there is another way possible.

Answer 10

@FutureMathProfessor uh, that's very wrong