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CBSE Class 12-science Answered

What is the integration x/(1+x tanx) ??  
Asked by deepukumarjatoliya | 28 Jan, 2019, 09:28: PM
answered-by-expert Expert Answer
begin mathsize 16px style integral fraction numerator x space d x over denominator 1 plus x space tan x end fraction space equals space integral fraction numerator x space cos x space d x over denominator cos begin display style space end style begin display style x end style begin display style space end style begin display style plus end style begin display style space end style begin display style x end style begin display style space end style begin display style sin end style begin display style x end style end fraction
l e t space u space equals space cos space x space plus space x space sin x
d u space equals space left parenthesis negative sin space x space plus space x space cos space x space plus space sin space x right parenthesis space d x space equals space x space cos x space d x
integral fraction numerator d u over denominator u end fraction space equals space log left parenthesis u right parenthesis space plus C space space equals space log left parenthesis cos space x space plus space x space sin x right parenthesis space plus space C end style
Answered by Thiyagarajan K | 28 Jan, 2019, 11:47: PM
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