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

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!)]