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CBSE Class 12-science Answered

Integration { 1/log x – 1/(log x )2}dx explain in great detail
Asked by haroonrashidgkp | 28 Oct, 2018, 01:06: PM
answered-by-expert Expert Answer
integral left parenthesis fraction numerator 1 over denominator log space x end fraction minus fraction numerator 1 over denominator left parenthesis log space x right parenthesis squared end fraction right parenthesis space d x

l e t space log space x equals space t
h e n c e space 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 t
w e space g e t space d x equals e to the power of t d t

integral left parenthesis fraction numerator 1 over denominator log space x end fraction minus fraction numerator 1 over denominator left parenthesis log space x right parenthesis squared end fraction right parenthesis space d x equals space integral e to the power of t left parenthesis 1 over t minus 1 over t squared right parenthesis space d t

w e space h a v e space integral e to the power of t left parenthesis f left parenthesis t right parenthesis plus f apostrophe left parenthesis t right parenthesis right parenthesis space d t equals space e to the power of space t space end exponent f left parenthesis t right parenthesis plus c
integral e to the power of t left parenthesis 1 over t minus 1 over t squared right parenthesis space d t equals e to the power of t space 1 over t space plus c space equals space e to the power of log space x end exponent space left parenthesis fraction numerator 1 over denominator log space x end fraction right parenthesis space plus c space
equals fraction numerator x over denominator log space space x end fraction plus c
Answered by Ram Singh | 28 Oct, 2018, 02:22: PM
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