# Convergence integrals

$\int_{15}^{\infty} \frac{-6x^4-7x^2+1}{7x^4-x^3+x}dx$

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• @Phia: What details do you need?

• I added some more detail. Let me know if you need any clarifications, but the solution is pretty much what I have written.

• Can you explain why the integral converges if the lim is 0?

• I am not saying that he integral converges if the lim is 0. If the limit is not zero then the integral is divergent. This is a well known fact about improper integrals which can be easily found in any calculus textbook.