First slide

Introduction to integration

Question

$\int (\sec x + \tan x)^{2} d x =$

Easy

A

$2 (\sec x + \tan x) - x + c$
B

$1 / 3 (\sec x + \tan x)^{3} + c$
C

$\sec x (\sec x + \tan x) + c$
D

$2 (\sec x + \tan x) + c$

Solution

$\begin{aligned} \int (\sec x + \tan x)^{2} dx = \int (\sec^{2} x + \tan^{2} x + 2 \sec xtan x) dx \\ = \int (2 \sec^{2} x - 1 + 2 \sec xtan x) dx \\ = 2 (\sec x + \tan x) - x + c \end{aligned}$

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