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CBSE Class 12-science Answered

Integration log x dx/( 1 + log x )2 explain in great detail
Asked by haroonrashidgkp | 28 Oct, 2018, 01:05: PM
answered-by-expert Expert Answer
integral fraction numerator log x over denominator left parenthesis 1 plus log space x right parenthesis squared end fraction d x l e t space space log space x equals t x equals e to the power of t d i f f e r e n t i a t e space w. r. t space space t w e space g e t space d x equals e to the power of t space d t integral fraction numerator begin display style log x end style over denominator begin display style left parenthesis 1 plus log space x right parenthesis squared end style end fraction d x equals integral e to the power of t left parenthesis fraction numerator t over denominator left parenthesis 1 plus t right parenthesis squared end fraction right parenthesis space d t integral e to the power of t left parenthesis fraction numerator t plus 1 minus 1 over denominator left parenthesis 1 plus t right parenthesis to the power of 2 space end exponent end fraction right parenthesis d t integral e to the power of t left parenthesis fraction numerator t plus 1 over denominator left parenthesis 1 plus t right parenthesis squared end fraction minus fraction numerator 1 over denominator left parenthesis 1 plus t right parenthesis squared end fraction right parenthesis space d t integral e to the power of t left parenthesis fraction numerator begin display style 1 end style over denominator begin display style left parenthesis 1 plus t right parenthesis end style end fraction minus fraction numerator begin display style 1 end style over denominator begin display style left parenthesis 1 plus t right parenthesis squared end style end fraction right parenthesis space d t w e space h a v e space integral e to the power of x space left parenthesis f left parenthesis x right parenthesis plus f apostrophe left parenthesis x right parenthesis right parenthesis d t space equals space e to the power of x space f left parenthesis x right parenthesis plus c integral e to the power of t left parenthesis fraction numerator begin display style 1 end style over denominator begin display style left parenthesis 1 plus t right parenthesis end style end fraction minus fraction numerator begin display style 1 end style over denominator begin display style left parenthesis 1 plus t right parenthesis squared end style end fraction right parenthesis space d t equals e to the power of t space end exponent fraction numerator 1 over denominator 1 plus t end fraction plus c equals fraction numerator x over denominator 1 plus log space x end fraction plus c
Answered by Ram Singh | 28 Oct, 2018, 04:32: PM

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