First slide

Methods of integration

Question

If $\int \tan^{4} x d x = K \tan^{3} x + L \tan x + f (x)$ , then

Easy

A

$K = 2 / 3$
B

$L = - 2$
C

$f (x) = x + C$
D

$K = 4 / 3$

Solution

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

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