First slide

Introduction to integration

Question

$\int \sin 2 x d (T a n x) =$

Easy

A

$\log |\sec x| + c$
B

$2 \log |\sec x| + c$
C

$\log |\cos x| + c$
D

$2 \log |\cos x| + c$

Solution

$\begin{array}{l} I = \int \sin 2 x d (\tan x) = \int 2 \sin x \cos x \sec^{2} x d x = \\ \int 2 \tan x d x = 2 \log | \sec x | + C \end{array}$

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