Question
find the derivative of
y= sigma (top number is x and bottom number is square root of x) e^t/t dt
please and thank you
y= sigma (top number is x and bottom number is square root of x) e^t/t dt
please and thank you
Answers
Damon
integral (e^t/t) dt
= ln t + t + +t^2/2*2! + x^3/3*3! ....
now limits, value at x - value at sqrt x
= ln x-lnx^1/2+x-x^1/2+x^2/2*2!-x/2*2!+x^3/3*3!-x^3/2/3*3! .....
= (1/2)lnx +series (x^n-x^n/2)[n/(n*n!)]
= ln t + t + +t^2/2*2! + x^3/3*3! ....
now limits, value at x - value at sqrt x
= ln x-lnx^1/2+x-x^1/2+x^2/2*2!-x/2*2!+x^3/3*3!-x^3/2/3*3! .....
= (1/2)lnx +series (x^n-x^n/2)[n/(n*n!)]