First slide

Introduction to integration

Question

$\int \frac{\sec x d x}{\sqrt{\cos 2 x}} =$

Easy

A

$\sin^{- 1} (\tan x) + c$
B

$\tan x + c$
C

$\cos^{- 1} (\tan x) + c$
D

$\frac{\sin x}{\sqrt{\cos x}} + c$

Solution

$\int \frac{\sec x d x}{\sqrt{\cos 2 x}} = \int \frac{\sec x}{\sqrt{\cos^{2} x - \sin^{2} x}} d x$
$\begin{aligned} = \int \frac{\sec^{2} x d x}{\sqrt{1 - \tan^{2} x}} \\ l e t \tan x = t s e c^{2} x d x = d t \\ = \sin^{- 1} (\tan x) + c \end{aligned}$

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