this qn (as told by my teacher) was asked 1ce in about 10yrs in d boards
nd tat ther is a chance of it cummin,nd also asked a decade ago in IIT
x2 dx
( xsinx + cosx)
VARSHA KRISHNAN....
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IIT is always a word which rises E thru' d body. But 2 achieve it U hav 2 drain out d entire E out of the body....
I think you have made a little mistake it should be ( x sin x + cos x) 2 in the denominator :
If by any chance that is the question then you have to multiply the numerator and deno by x cos x that i think will be the shortest method though there are other methods of approach too!
x2/x cos x . (x cos x)/( x sin x + cosx) 2 dx
= x sec x . x cos x / ( x sin x + cos x)2 dx
= x sec x x cos x/ ( x sin x + cos x)2 dx - d/dx(x sec x)[ x cos x/ ( x sin x + cos x) 2] dx
= - x sec x / (x sin x + cos x) - (sec x + x sec x tan x)(-1/xsin x + cos x) dx
= - x sec x/ (x sin x + cos x) + sec 2 x(x sin x + cos x ) / (x sin x+ cos x)dx
= - x sec x/ (x sin x + cos x) + tan x . ans.
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From J.R.R. Tolkien's 'The Lord of the Rings':
All that is gold does not glitter
Not all who wander are lost
The old that is strong does not wither,
Deep roots are not reached by frost.
From ashes a fire shall be woken
From shadows a light shall spring
Renewed shall be blade that's broken
The crown less again shall be king.
Moderation Team
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89
x2 dx 
x2/x cos x . (x cos x)/( x sin x + cosx) 2 dx 
