First slide

Introduction to integration

Question

$\int \frac{1}{1 - \sin x} d x$

Easy

A

$\cot x + \cos e c x + c$
B

$\tan x - \sec x + c$
C

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

$\cot x - \cos e c x + c$

Solution

$\begin{array}{l} = \int \frac{1}{1 - \sin x} d x \\ = \int (\frac{1}{1 - \sin x}) (\frac{1 + \sin x}{1 + \sin x}) d x \\ = \int \frac{1 + \sin x}{\cos^{2} x} d x \\ = \int [\frac{1}{\cos^{2} x} + \frac{\sin x}{\cos x} \cdot \frac{1}{\cos x}] d x \end{array}$
$= \tan x + \sec x + c$

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