First slide

Introduction to integration

Question

$\int \frac{\tan x - \tan \frac{x}{2}}{1 + \tan x . \tan \frac{x}{2}} d x =$

Easy

A

$\log | \sec \frac{x}{2} | + C$
B

$\frac{1}{2} \log | \sec \frac{x}{2} | + C$
C

$2 \log | \sec \frac{x}{2} | + C$
D

$\frac{1}{4} \log | \sec \frac{x}{2} | + C$

Solution

$\int \frac{\tan x - \tan \frac{x}{2}}{1 + \tan x . \tan \frac{x}{2}} d x$    = $\int \tan (x - \frac{x}{2}) d x$
                                     $= \int \tan (\frac{x}{2}) d x$

                                     $= 2 \log | \sec \frac{x}{2} | + C$

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