First slide

Methods of integration

Question

$\int \frac{\sec^{2} x}{\log {(\tan x)}^{\tan x}} d x =$

Easy

A

$\log | \tan x | + C$
B

$\log | \log (\tan x) | + C$
C

$\frac{1}{\log (\tan x)} + C$
D

$\frac{\tan x}{\log | \tan x |} + C$

Solution

       $\int \frac{\sec^{2} x}{\tan x \log (\tan x)} d x$
         $\log (\tan x) = t$

        $\int \frac{1}{t} d t = \log t + C$

                 $= \log | \log (\tan x) | + C$

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