How do I solve this indefinite integral?

Question

Given the improper integral: $$\int_1^\infty 45\frac{x+1}{x^2+2x} \, dx$$ I was able to set up the limits as shown below, but I am not sure how to continue integrating. $$\lim_{t\to\infty}\int_1^t 45\frac{x+1}{x^2+2x} \, dx = \lim_{t\to\infty} 45 \int_1^t \frac{x+1}{x^2+2x} \, dx$$

Answer 1

By $u$-substitution, $u=x^2+2x.$