First slide

Introduction to integration

Question

$\int {\{1 + 2 \tan x (\tan x + \sec x)\}}^{1 / 2} d x$

Moderate

A

$\log (\sec x (\sec x - T a n x)) + C$
B

$\log |S e c x (S e c x + T a n x)| + C$
C

$\log |S e c x (T a n x - S e c x)| + C$
D

$\log |T a n x (S e c x - T a n x)| + C$

Solution

$\int {(1 + 2 \tan^{2} x + 2 \tan x \sec x)}^{1 / 2} d x$
$\begin{array}{l} = \int {(\sec^{2} x + \tan^{2} x + 2 \tan c \sec x)}^{1 / 2} d x \\ = \int (\sec^{} x + \tan x) d x \\ = \log | \sec x + \tan x | + \log | \sec x | + c \\ = \log | \sec x (\sec x + \tan x) | + c \end{array}$

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