Answer
$$\int\frac{1}{r}\csc^2(1+\ln r)dr=-\cot(1+\ln r)+C$$
Work Step by Step
$$A=\int\frac{1}{r}\csc^2(1+\ln r)dr$$
We set $a=1+\ln r$, which means $$da=\frac{1}{r}dr$$
Therefore, $$A=\int\csc^2ada $$ $$A=-\cot a+C$$ $$A=-\cot(1+\ln r)+C$$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 5 - Practice Exercises - Page 343: 60
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