Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 7 - Section 7.1 - Integration by Parts - 7.1 Exercises: 13

Answer

$= - t\cot t + \ln |\sin t| +C$

Work Step by Step

$\int t (\csc^{2}t) dx$ $u = t$ $u' = 1$ $\frac{du}{dt} = 1$ $du = 1 dt$ $du = dt$ $dv = (\csc^{2}t)$ $v = - \cot t$ $uv - \int vdu$ $= (t)(- \cot t) - \int (- \cot t)dt$ $= (t)(- \cot t) + \int (\cot t)dt$ $= (t)(- \cot t) + \ln |\sin t| +C$ $= - t\cot t + \ln |\sin t| +C$
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