First slide

Methods of integration

Question

$\int \tan^{2} x \sec^{4} x d x$

Easy

A

$\frac{\tan^{3} x}{3} + \frac{\tan^{5} x}{5} + C$
B

$\frac{\tan^{3} x}{3} - \frac{\tan^{5} x}{5} + C$
C

$- \frac{\tan^{3} x}{3} - \frac{\tan^{5} x}{5} + C$
D

$\frac{\tan^{6} x}{6} + \frac{\tan^{4} x}{4} + C$

Solution

$\begin{array}{l} \tan x = t \sec^{2} x d x = d t \\ \int t^{2} (1 + t^{2}) d t = \int (t^{2} + t^{4}) d t \\ = \frac{t^{3}}{3} + \frac{t^{5}}{5} + C \end{array}$

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