Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 7: Transcendental Functions - Section 7.7 - Hyperbolic Functions - Exercises 7.7 - Page 430: 50

Answer

$-csch(\ln t) +C$

Work Step by Step

As we are given that $\int \dfrac{csch(\ln t) coth(\ln t) dt}{ t}$ Re-write: $\int \dfrac{csch(\ln t) coth(\ln t) dt}{ t}= \int [csch(\ln t) coth(\ln t)](\dfrac{ dt}{ t})$ Now, consider $\ln t =a$ and $da= \dfrac{ dt}{ t}$ This implies , $\int csch(\ln t) coth(\ln t)(\dfrac{ dt}{ t})= \int (csch a ) (coth a) da=- csch a +C=-csch(\ln t) +C$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.