Question

Integrate 1 / (x^10 + x)


1

Answer 1

I'm not sure about the best way to approach this one.

Answer 2

partial fractions does n't help

Answer 3

multiply top and bottom by \(x^{-10}\) :

\[\int \dfrac{x^{-10}}{1+x^{-9}}\,dx\]

Answer 4

ah!!!

Answer 5

next step is obvious
sub \(u = 1+x^{-9}\)

Answer 6

so its -1/9 ln (1 + x^-9)?

Answer 7

looks good !

Answer 8

thank you

Answer 9

np

Answer 10

integration is an art...

Answer 11

definitely almost every integration problem requires guessing and makes mathematicians feel humble of the fact that we can't integrate everything into an elementary function ;)

Answer 12

too true