CBSE Class 12-science Answered
Integration log x dx/( 1 + log x )2 explain in great detail
Asked by haroonrashidgkp | 28 Oct, 2018, 13:05: PM
![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](https://images.topperlearning.com/topper/tinymce/cache/e5dfd1158ea212893df17f20ff6a1b00.png)
Answered by Ram Singh | 28 Oct, 2018, 16:32: PM
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