![\int \limits_1^{\infty}\frac{\ln x}{x^2}\,dx=\lim_{t\to\infty}\int \limits_1^t \frac{\ln x}{x^2}\\\\ \int \frac{\ln x}{x^2}\,dx=(*)\\ u=\ln x,du=\frac{1}{x} \\ dv=\frac{1}{x^2},v=-\frac{1}{x}\\ (*)=\ln x\cdot(-\frac{1}{x})-\int (\frac{1}{x}\cdot(-\frac{1}{x}))\, dx=\\ -\frac{\ln x}{x}+\int\frac{1}{x^2}\, dx=\\ -\frac{\ln x}{x}-\frac{1}{x}+C\\\\ \lim_{t\to\infty}\int \limits_1^t \frac{\ln x}{x^2}=\lim_{t\to \infty}\left[-\frac{\ln x}{x}-\frac{1}{x} \right]_1^t=](/tpl/images/0187/7657/b30cd.png)
Look at the photo and give the ansver.
...
Answers: 1
Another question on Mathematics
Mathematics, 21.06.2019 18:20
Alana has 12.5 cups of flour with which she is baking four loaves of raisin bread and one large pretzel. the pretzel requires 2.5 cups of flour to make. how much flour is in each loaf of raisin bread? explain the steps to follow to get the answer.
Answers: 3
Mathematics, 21.06.2019 19:30
Factor the expression using the gcf. the expression 21m−49n factored using the gcf
Answers: 2
Mathematics, 21.06.2019 21:00
The function below show how much jayna and hannah charge for babysitting. which statement best compares the two plants?
Answers: 1
Mathematics, 22.06.2019 01:30
A23 – year – old male buys 100/300/100 liability insurance, collision insurance with a $100 deductible, and comprehensive insurance with a $250 deductible? what is his total annual premium? (a) $1142.00 (b) $1765.45 (c) $1770.10 (d) $1785.25
Answers: 2
You know the right answer?
Questions
Mathematics, 14.12.2021 22:20
Mathematics, 14.12.2021 22:20
Mathematics, 14.12.2021 22:20
Biology, 14.12.2021 22:20
Mathematics, 14.12.2021 22:20
Physics, 14.12.2021 22:20
Mathematics, 14.12.2021 22:20
Chemistry, 14.12.2021 22:20
Mathematics, 14.12.2021 22:20
English, 14.12.2021 22:20
English, 14.12.2021 22:20
Health, 14.12.2021 22:20
Mathematics, 14.12.2021 22:20
English, 14.12.2021 22:20
