## welshfella one year ago Integrate 1 / (x^10 + x) 1

1. welshfella

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

2. welshfella

partial fractions does n't help

3. ganeshie8

multiply top and bottom by $$x^{-10}$$ : $\int \dfrac{x^{-10}}{1+x^{-9}}\,dx$

4. welshfella

ah!!!

5. ganeshie8

next step is obvious sub $$u = 1+x^{-9}$$

6. welshfella

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

7. ganeshie8

looks good !

8. welshfella

thank you

9. ganeshie8

np

10. welshfella

integration is an art...

11. ganeshie8

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 ;)

12. welshfella

too true