Integration x2 tan-1 x/( 1 + x2)dx explain in great detail

Asked by haroonrashidgkp | 21st Oct, 2018, 03:37: PM

Expert Answer:

begin mathsize 16px style straight I equals integral fraction numerator straight x squared tan to the power of negative 1 end exponent straight x over denominator 1 plus straight x squared end fraction dx
tan to the power of negative 1 end exponent straight x equals straight t rightwards double arrow straight x equals tant
fraction numerator 1 over denominator 1 plus straight x squared end fraction dx equals dt
straight I equals integral open parentheses tan squared straight t close parentheses tdt
straight I equals integral straight t open parentheses sec squared straight t minus 1 close parentheses dt
straight I equals integral open parentheses tsec squared straight t minus straight t close parentheses dt
Integrate space further. end style

Answered by Sneha shidid | 21st Oct, 2018, 06:31: PM

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