First slide

Methods of integration

Question

$\int \cot^{3} x \cos e c^{- 8} x d x$

Easy

A

$\frac{\sin^{6} x}{6} - \frac{\sin^{8} x}{8} + C$
B

$\frac{\sin^{6} x}{6} + \frac{\sin^{8} x}{8} + C$
C

$\frac{\cos^{6} x}{6} - \frac{\cos^{8} x}{8} + C$
D

$\frac{\cos^{6} x}{6} + \frac{\cos^{8} x}{8} + C$

Solution

$\begin{array}{l} cosec x = t \Rightarrow (cosec x \cot x) d x = - d t \\ \int \frac{(t^{2} - 1) (- d t)}{t^{9}} = - \int \frac{1}{t^{7}} d t + \int \frac{1}{t^{9}} d t \\ = \frac{1}{6 t^{6}} - \frac{1}{8 t^{8}} + C \end{array}$

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