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CBSE Class 12-science Answered

Integration ex [ sec x + log( sec x + tan x )] dx explain in great detail
Asked by haroonrashidgkp | 25 Oct, 2018, 10:39: AM
answered-by-expert Expert Answer
begin mathsize 16px style straight I equals integral straight e to the power of straight x open parentheses secx plus log space open parentheses sec space straight x space plus space tan space straight x close parentheses close parentheses dx
Consider comma space straight f left parenthesis straight x right parenthesis space equals log space open parentheses sec space straight x space plus space tan space straight x close parentheses space then space
straight f apostrophe left parenthesis straight x right parenthesis space equals space fraction numerator 1 over denominator sec space straight x space plus space tan space straight x end fraction cross times open parentheses sec space straight x space tan space straight x space plus space sec squared space straight x close parentheses
straight f apostrophe left parenthesis straight x right parenthesis equals fraction numerator sec space straight x over denominator sec space straight x space plus space tan space straight x end fraction cross times open parentheses tan space straight x space plus space sec space straight x close parentheses
straight f apostrophe left parenthesis straight x right parenthesis space equals sec space straight x
Hence comma space using space integral straight e to the power of straight x left parenthesis straight f left parenthesis straight x right parenthesis space plus space straight f apostrophe left parenthesis straight x right parenthesis right parenthesis dx equals straight e to the power of straight x straight f left parenthesis straight x right parenthesis plus straight c
straight I equals straight e to the power of straight x log space open parentheses sec space straight x space plus space tan space straight x close parentheses plus straight c end style
Answered by Sneha shidid | 25 Oct, 2018, 10:58: AM
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