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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
0 votes

Integrate : $\int \large\frac{\sec x cosec x}{\log (\tan x )}$$dx$

$(a)\;\log _e | \log (\tan x) |+c \\(b)\;\log _e | \log (\cos x) |+c \\(c)\;\log (\sin x +c) \\ (d)\;None$

Can you answer this question?
 
 

1 Answer

0 votes
$\log (\tan x)=t$
differentiate with respect to x
$\large\frac{1}{\tan x }.$$\sec^2 x dx =dt$
=> $ \large\frac{\sec x \cos x }{\cos x \sin x}$$dx=dt$
=> $\sec x \;cosec x dx=dt$
$\int \large\frac{dt}{t}=$$\log _e | \log (\tan x) |+c$
Hence a is the correct answer.
answered Dec 30, 2013 by meena.p
 
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