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Home / Doubts and Solutions/JEE/Mathematics

Integration of e^tan^-1x{1+x^2+x÷1+x^2}

Asked by khedejalaj7 28th August 2018, 7:17 PM
Answered by Expert
Answer:
begin mathsize 16px style straight I equals integral straight e to the power of tan to the power of negative 1 end exponent straight x end exponent open parentheses fraction numerator 1 plus straight x plus straight x squared over denominator 1 plus straight x squared end fraction close parentheses dx tan to the power of negative 1 end exponent straight x equals straight t straight x equals tant dx equals sec squared tdt straight I equals integral straight e to the power of straight t open parentheses fraction numerator 1 plus tant plus tan squared straight t over denominator 1 plus tan squared straight t end fraction close parentheses sec squared tdt straight I equals integral straight e to the power of straight t open parentheses fraction numerator 1 plus tant plus tan squared straight t over denominator sec squared straight t end fraction close parentheses sec squared tdt straight I equals integral straight e to the power of straight t open parentheses 1 plus tan squared straight t plus tant close parentheses dt straight I equals integral straight e to the power of straight t open parentheses tant plus sec squared straight t close parentheses dt straight I equals straight e to the power of straight t tant plus straight c straight I equals xe to the power of tan to the power of negative 1 end exponent straight x end exponent plus straight c end style
Answered by Expert 29th August 2018, 9:53 AM
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Tags: integration-examples problems-on-integration integration-by-substituion integration
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