Question

whats the integral for x^4 / (1-x) ??

Answer 1

Try to get some common fractions from this integrand.

Answer 2

i would have written
(x^4-1)+1 as numerator
then separate the numerator,-[ (x^4-1)/(x-1) +1/(x-1)]
2nd term is easy to integrate.
for 1st term, you can cancel out common factor of (x-1) from numerator and denominator.

Answer 3

if you know how to factorize x^4-1

Answer 4

Hint:\[x^4=x^4-1+1=(x^2-1)(x^2+1)+1=(x-1)(x+1)(x^2+1)-1.\]

Answer 5

^

Answer 6

or make a substitution as u=1-x