x/(x+4)^-1/2 integration

Asked by tushantyadav63224 | 30th Aug, 2020, 09:43: PM

Expert Answer:

TO integrate:
x/(x+4)-1/2
Let space straight I equals integral straight x over left parenthesis straight x plus 4 right parenthesis to the power of negative 1 divided by 2 end exponent dx equals integral straight x square root of straight x plus 4 end root dx
Take space straight x plus 4 equals straight t rightwards double arrow dx equals dt
straight I equals integral left parenthesis straight t minus 4 right parenthesis square root of straight t space dt equals integral straight t to the power of 3 divided by 2 end exponent space dt space minus space 4 integral straight t to the power of 1 divided by 2 end exponent space dt
equals fraction numerator straight t to the power of 5 divided by 2 end exponent over denominator 5 divided by 2 end fraction minus 4 fraction numerator straight t to the power of 3 divided by 2 end exponent over denominator 3 divided by 2 end fraction
equals 2 over 5 straight t to the power of 5 divided by 2 end exponent minus 8 over 3 straight t to the power of 3 divided by 2 end exponent
equals 2 over 5 open parentheses straight x plus 4 close parentheses to the power of 5 divided by 2 end exponent minus 8 over 3 open parentheses straight x plus 4 close parentheses to the power of 3 divided by 2 end exponent

Answered by Renu Varma | 31st Aug, 2020, 12:09: PM