First slide

Introduction to integration

Question

$\int \frac{\tan x}{\sqrt{\sin^{4} x + \cos^{4} x}} d x$ is equal to

Moderate

A

$\log (\tan^{2} x + \sqrt{1 + \tan^{4} x}) + C$
B

$\frac{1}{2} \log (\tan^{2} x + \sqrt{1 + \tan^{4} x}) + C$
C

$\frac{1}{4} \log (\tan^{2} x + \sqrt{1 + \tan^{4} x}) + C$
D

None of these

Solution

$\int \frac{\tan x}{\sqrt{\sin^{4} x + \cos^{4} x}} d x = \int \frac{\tan x . \sec^{2} x}{\sqrt{1 + \tan^{4} x}} d x$
$= \frac{1}{2} \int \frac{d z}{\sqrt{1 + z^{2}}}$

(Putting $\tan^{2} x = z \Rightarrow \tan x . \sec^{2} x d x = \frac{1}{2} d z$ )

$= \frac{1}{2} \log (z + \sqrt{1 + z^{2}}) + C$

$= \frac{1}{2} \log (\tan^{2} x + \sqrt{1 + \tan^{4} x}) + C .$

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