First slide

Methods of integration

Question

$\int e^{x} \sec x (1 + \tan x) dx$ is equal to

Easy

A

$e^{x} \cos x + C$
B

$e^{x} \sec x + C$
C

$e^{x} \sin x + C$
D

$e^{x} \tan x + C$

Solution

Let $I = \int e^{x} \sec x (1 + \tan x) dx$
$\Rightarrow I = \int e^{x} \sec xdx + \int e^{x} \sec xtan xdx - - - - - (i)$
Now $\int e^{x} \sec xdx = \sec x \int e^{x} dx - \int [\frac{d}{dx} \sec x \int e^{x} dx] dx$
$= e^{x} \sec x - \int \sec xtan {xe}^{x} dx - - - - (ii)$
$On putting the value from Eq . (ii) inEq . (i), we get$
$\begin{array}{l} I = e^{x} \sec x - \int e^{x} \sec xtan xdx + \int \sec xtan {xe}^{x} dx + C \\ \Rightarrow I = e^{x} \sec x + C \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App