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Integrate xtan^-1 w.r.t x.
Asked by leelanarendra255 | 25 May, 2019, 05:49: PM
answered-by-expert Expert Answer
L e t space I equals integral x tan to the power of negative 1 end exponent x space d x equals tan to the power of negative 1 end exponent x integral x space d x minus integral open parentheses open parentheses integral x space d x close parentheses fraction numerator d open parentheses tan to the power of negative 1 end exponent x close parentheses over denominator d x end fraction close parentheses d x equals x squared over 2 tan to the power of negative 1 end exponent x minus integral open parentheses x squared over 2 times fraction numerator 1 over denominator 1 plus x squared end fraction close parentheses d x equals x squared over 2 tan to the power of negative 1 end exponent x minus 1 half integral open parentheses 1 minus fraction numerator 1 over denominator 1 plus x squared end fraction close parentheses d x equals x squared over 2 tan to the power of negative 1 end exponent x minus 1 half open parentheses integral 1 d x minus integral fraction numerator 1 over denominator 1 plus x squared end fraction d x close parentheses equals x squared over 2 tan to the power of negative 1 end exponent x minus 1 half open parentheses x minus tan to the power of negative 1 end exponent x close parentheses equals x squared over 2 tan to the power of negative 1 end exponent x minus 1 half x plus 1 half tan to the power of negative 1 end exponent x
Answered by Renu Varma | 27 May, 2019, 11:06: AM

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