Answer
$$\frac{1}{5}$$
Work Step by Step
\begin{align*}
\int_{\pi / 4}^{3 \pi / 4} \cot ^{4} x \csc ^{2} x d x&=-\frac{1}{5}\cot ^{5} x\bigg|_{\pi / 4}^{3 \pi / 4} \\
&=\frac{1}{5}
\end{align*}
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 8 - Techniques of Integration - 8.2 Trigonometric Integrals - Exercises - Page 403: 58
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