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

yep, but how can I solve it?

what u mean with rational expression?

Fraction. Fancy word for fraction.

??

Unfortunately not that simple. u was in your denominator, wasn't it?

??

Okay, much better. But you cannot solve this integral without expressing \(x^4\) in terms of u.

so.. what can I do??

Well
\[\large u = 1-x\]
\[\large x = 1-u\]
\[\huge x^4 = (1-u)^4\]

wow! so uhm,, what do I have to do now?

Expand.

\[\large (1-u)^4 = u^4 -4u^3 +6u^2 -4u +1\]

mm so what I = to "u" then? :/