I did my very best to do and redo by equation over and over, yet I cant get beyond this result. I'm not sure if the answer given at the back of my book is wrong or I am. Please help!!!!!!!!!.
2026-04-22 16:05:37.1776873937
Partial Fractions in Integration
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Up until you have $$\lim_{b\to\infty}\frac{1}{3}\int_{0}^{b}\frac{2}{2x+1}-\frac{1}{x+2}dx$$Your solution was correct.Then you would get$$\lim_{b\to\infty}\frac{1}{3}(\ln(\frac{2b+1}{b+2})+\ln2)$$ So a nuisance is the plus instead of minus. But that's not what changed your answer, I think you forgot to add the $\ln2$ resulting from the lower bound in the integral. If you add both of the $\ln2$s, you would get the desired answer, $\frac{2\ln2}{3}$