Integrate x/(1-x)^54

Asked by Harshgupta343260 | 25th Aug, 2019, 05:18: PM

Expert Answer:

begin mathsize 16px style straight I equals integral subscript 0 superscript 1 space straight x over open parentheses 1 minus straight x close parentheses to the power of 54 dx end style
begin mathsize 16px style straight I equals integral subscript 0 superscript 1 space fraction numerator 1 minus straight x over denominator straight x to the power of 54 end fraction dx space space space space space space space space space space space space space space using space integral subscript 0 superscript straight a space straight f open parentheses straight x close parentheses dx equals integral subscript 0 superscript straight a straight f open parentheses straight a minus straight x close parentheses dx end style
begin mathsize 16px style straight I equals integral subscript 0 superscript 1 space open parentheses straight x to the power of negative 54 end exponent minus straight x to the power of negative 53 end exponent close parentheses dx end style
Integrating this you will get the answer.

Answered by Sneha shidid | 26th Aug, 2019, 09:49: AM

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