First slide

Methods of integration

Question

The $\int \frac{\sin^{2} x}{\cos^{6} x} d x$ is a

Easy

A

$is a polynomial of degree 5 in \sin x$
B

$is a polynomial of degree 4 in \tan x$
C

$is a polynomial of degree 5 in \tan x$
D

$is a polynomial of degree 5 in \cos x$

Solution

Putting $\tan x = t$ the given integral can be written as
$\int t^{2} (1 + t^{2}) d t = \frac{t^{3}}{3} + \frac{t^{5}}{5} + C = \frac{\tan^{5} x}{5} + \frac{\tan^{3} x}{3} + C$
which is a polynomial of degree 5 in $\tan x$

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