First slide

Introduction to integration

Question

$\int \sin 2 x d (\tan x) is equal to$

Easy

A

$2 \ln | \cos x | + C$
B

$\ln | \cos x | + C$
C

$2 \ln | \sec x | + C$
D

$\ln | \sec x | + C$

Solution

$\begin{aligned} I = \int \sin 2 x \cdot d (\tan x) = \int \sin 2 x \cdot \sec^{2} x d x = 2 \int \tan x d x \\ = 2 \ln | \sec x | + C \end{aligned}$

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