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###### H Sampada posted an Question
September 24, 2021 • 13:02 pm 30 points
• IIT JAM
• Physics (PH)

# Sin x cosx cos'x+ 3 cos x +2 dx equals put cos x t, then tdt t dt p+3t+2t1(t+2) 2 dt t+2 t+1 =[2 log (t+2)-log(t+1)), = 2 log 3- log 2-2 log 2 + log1=log (9

sin x cosX cos'x+ 3 cos x +2 dx equals Put cos x t, then tdt t dt P+3t+2t1(t+2) 2 dt t+2 t+1 =[2 log (t+2)-log(t+1)), = 2 log 3- log 2-2 log 2 + log1=log (9 /8) please explain this problem

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• ##### H sampada

And how to identify the properties?

You have to first see the properties of definite integrals and then just applied on problems. There are not many properties, only you have to memorize Two or three properties and they are used mostly in Questions. After practise you can easily identify which property are used in the particular Question.

ok sir

• ##### H sampada

sir please explain last 3 steps

First i integrate the function and then I used the log property. log(a) + log(b) = log(ab).,....... alog(b) = log(a^b)

• ##### Anshum Sharma

Here is the detailed solution

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