(2x+1)²/x-2,Integrate the given function defined on proper domain w.r.t. x.
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In the attachment I have answered this problem. I have applied decomposition method to find the anti derivative of the given function. See the attachment for detailed solution.
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HELLO DEAR,
PUT (x - 2) = t so dx = dt
AND x - 2 = t => 2x = 2t + 4
therefore, ∫(2t + 4)²/t .dt
=> I = ∫(4t² + 16 + 16t)/t .dt
=> I = 4∫t.dt + 16∫dt/t + 16∫.dt
=> I = 4t²/2 + 16log|t| + 16t + C.
put t = (x - 2).
=> I = 2(x - 2)² + 16log|x - 2| + 16(x - 2) + C.
I HOPE ITS HELP YOU DEAR,
THANKS
PUT (x - 2) = t so dx = dt
AND x - 2 = t => 2x = 2t + 4
therefore, ∫(2t + 4)²/t .dt
=> I = ∫(4t² + 16 + 16t)/t .dt
=> I = 4∫t.dt + 16∫dt/t + 16∫.dt
=> I = 4t²/2 + 16log|t| + 16t + C.
put t = (x - 2).
=> I = 2(x - 2)² + 16log|x - 2| + 16(x - 2) + C.
I HOPE ITS HELP YOU DEAR,
THANKS
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