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CBSE Class 12-science Answered

 Integration x cot-1 x dx explain in great detail
Asked by haroonrashidgkp | 22 Oct, 2018, 02:09: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight I equals integral xcot to the power of negative 1 end exponent xdx straight I equals integral open parentheses cot to the power of negative 1 end exponent straight x close parentheses xdx straight I equals cot to the power of negative 1 end exponent straight x integral xdx minus integral open parentheses straight d over dx cot to the power of negative 1 end exponent straight x integral xdx close parentheses dx straight I equals straight x squared over 2 cot to the power of negative 1 end exponent straight x minus integral fraction numerator negative 1 over denominator 1 plus straight x squared end fraction cross times straight x squared over 2 dx straight I equals straight x squared over 2 cot to the power of negative 1 end exponent straight x plus 1 half integral fraction numerator straight x squared over denominator 1 plus straight x squared end fraction dx straight I equals straight x squared over 2 cot to the power of negative 1 end exponent straight x plus 1 half integral open parentheses fraction numerator straight x squared plus 1 minus 1 over denominator 1 plus straight x squared end fraction close parentheses dx straight I equals straight x squared over 2 cot to the power of negative 1 end exponent straight x plus 1 half integral open parentheses 1 minus fraction numerator 1 over denominator 1 plus straight x squared end fraction close parentheses dx straight I equals straight x squared over 2 cot to the power of negative 1 end exponent straight x plus 1 half open parentheses straight x minus tan to the power of negative 1 end exponent straight x close parentheses plus straight c end style
Answered by Sneha shidid | 22 Oct, 2018, 05:57: PM

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