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​The value of the integral π/3 ∫ ((x sin x ) / (cos 2 x )) dx , is -π/3 (π/3 – log tan 3 pi/2) 2( 2pi/3- log tan 5pi/12) 3(pi/2-log sin pi/12) none of these

​The value of the integral 
π/3
  ∫    ((x sin x ) / (cos2x )) dx , is
-π/3
  1. (π/3 – log tan 3 pi/2)
  2. 2( 2pi/3- log tan 5pi/12)
  3. 3(pi/2-log sin pi/12)
  4. none of these

Grade:12

1 Answers

Sushant Kumar
42 Points
5 years ago
answer is 
  1. 2( 2pi/3- log tan 5pi/12)
 
 
π/3
  ∫    ((x sin x ) / (cos2x )) dx , is = -π/3
π/3
  ∫    ((x tanx secx )) dx   now take tanxsecx as 1ST  function and x as 2nd function as integration of tanxsecx is secx  
-π/3
 now take tanxsecx as 1ST  function and x as 2nd function as integration of tanxsecx is secx and diferentiation of x is dx
 
using integration by parts you will get the answer ( value of tan(5pi/12/)=2+sqrt(3)  )
 
hope this will help 

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