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CBSE Class 12-science Answered

Integration (x2 + 1)/(x4 + 1) dx explain in great detail
Asked by haroonrashidgkp | 05 Oct, 2018, 12:15: PM
answered-by-expert Expert Answer
begin mathsize 18px style integral fraction numerator straight x squared plus 1 over denominator straight x to the power of 4 plus 1 end fraction dx
divide space by space straight x squared
integral fraction numerator begin display style 1 plus 1 over straight x squared end style over denominator begin display style straight x squared plus fraction numerator begin display style 1 end style over denominator begin display style straight x squared end style end fraction end style end fraction dx
equals integral fraction numerator begin display style 1 plus 1 over straight x squared end style over denominator begin display style straight x squared plus fraction numerator begin display style 1 end style over denominator begin display style straight x squared end style end fraction minus 2 plus 2 end style end fraction dx
equals integral fraction numerator begin display style 1 plus 1 over straight x squared end style over denominator begin display style open parentheses straight x minus fraction numerator begin display style 1 end style over denominator begin display style straight x end style end fraction close parentheses squared plus 2 end style end fraction dx
straight x minus fraction numerator begin display style 1 end style over denominator begin display style straight x end style end fraction equals straight t
1 plus fraction numerator begin display style 1 end style over denominator begin display style straight x squared end style end fraction dx equals dt
equals integral fraction numerator begin display style 1 end style over denominator begin display style straight t squared plus 2 end style end fraction dt
equals fraction numerator 1 over denominator square root of 2 end fraction tan to the power of negative 1 end exponent open parentheses fraction numerator straight t over denominator square root of 2 end fraction close parentheses plus straight c
equals fraction numerator begin display style 1 end style over denominator begin display style square root of 2 end style end fraction tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style straight x minus fraction numerator begin display style 1 end style over denominator begin display style straight x end style end fraction end style over denominator begin display style square root of 2 end style end fraction close parentheses plus straight c end style
Answered by Arun | 08 Oct, 2018, 10:15: AM
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