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At 13:49, in the last step of the second sum, how did the sir seperate integral of [(t+1) - 1 divided by t(t+1)] into integral of (1/t) dt - integral of [1/(t+1)] dt ??

Asked by rj4fun 1st November 2017, 8:12 AM
Answered by Expert
Answer:
begin mathsize 16px style integral open parentheses fraction numerator open parentheses straight t plus 1 close parentheses minus 1 over denominator straight t open parentheses straight t plus 1 close parentheses end fraction close parentheses dt
integral open parentheses fraction numerator straight t plus 1 over denominator straight t open parentheses straight t plus 1 close parentheses end fraction minus fraction numerator 1 over denominator straight t open parentheses straight t plus 1 close parentheses end fraction close parentheses dt
integral open parentheses 1 over straight t minus fraction numerator begin display style 1 end style over denominator begin display style straight t open parentheses straight t plus 1 close parentheses end style end fraction close parentheses dt

NOTE colon
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end style
Answered by Expert 13th December 2017, 4:39 PM
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