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Plz give the proof of this equation:
Integration of tanx dx = -log lcosxl + c = log lsecxl + c?

Asked by dasratna_72 21st May 2017, 8:29 PM
Answered by Expert
Answer:
begin mathsize 16px style straight I equals integral tanx space dx
straight I equals integral sinx over cosx dx
If space straight f left parenthesis straight x right parenthesis equals cosx rightwards double arrow straight f apostrophe left parenthesis straight x right parenthesis equals negative sinx
straight I equals negative integral fraction numerator negative sinx over denominator cosx end fraction dx
straight I equals negative log open vertical bar cosx close vertical bar plus straight c
straight I equals log open parentheses cosx close parentheses to the power of negative 1 end exponent plus straight c
straight I equals log open vertical bar secx close vertical bar plus straight c end style
Answered by Expert 22nd May 2017, 8:59 AM
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