How do you find the power series for $f'(x)$ and $int f(t)dt$ from [0,x] given the function $f(x)=Sigma x^n/lnn$ from $n=[2,oo)$ ?

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Answer 1 · 2017-03-23T12:03:15

See below

For:

$f(x)=sum_(n = 2)^(oo) x^n/lnn$

We differentiate wrt x:

$f'(x)= sum_(n = 2)^(oo) (n x^(n-1))/lnn$

And:

$int_0^x f(t) \ dt = int_0^x sum_(n = 2)^(oo) t^n/lnn \ dt$

$= sum_(n = 2)^(oo) (x^(n+1))/((n+1) lnn )$

How do you find the power series for f'(x)f'(x) and int f(t)dtint f(t)dt from [0,x] given the function f(x)=Sigma x^n/lnnf(x)=Sigma x^n/lnn from n=[2,oo)n=[2,oo)?