First slide

Methods of integration

Question

If $\int \frac{x + \sin x}{1 + \cos x} d x = f (x) \tan \frac{x}{2} + C$ then

Easy

A

$f (x) = x^{2}$
B

$f (x) = x$
C

$f (x) = 1 + \cos x$
D

none of these

Solution

$\int \frac{x + \sin x}{1 + \cos x} d x = \frac{1}{2} \int x \sec^{2} \frac{x}{2} d x + \int \frac{\sin x}{1 + \cos x} d x$
$\begin{matrix} = \frac{1}{2} [2 x \tan \frac{x}{2} - 2 \int \tan \frac{x}{2}] + \int \tan \frac{x}{2} d x \\ = x \tan \frac{x}{2} + C . \end{matrix}$

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