# Math Help - Series/Taylor

1. ## Series/Taylor

Evaluate the integral as a power series. What is the radius of convergence?

1) integral of [ ln(1-t) / t ] dt

Evaluate the indefinite integral as an infinite series

2) integral of [(e^x-1)/x ]dx

Can someone show me how these are done? thank you

2. Originally Posted by xfyz

2) integral of [(e^x-1)/x ]dx

Can someone show me how these are done? thank you
$e^x = 1+x+x^2/2!+x^3/3!+...$
So,
$e^x - 1 = x+x^2/2!+x^3/3!+...$
Thus,
$(e^x-1)/x = 1 + x/2!+x^2/3!+...$
Now integrate term-by-term and what do you get?

3. Originally Posted by ThePerfectHacker
$e^x = 1+x+x^2/2!+x^3/3!+...$
So,
$e^x - 1 = x+x^2/2!+x^3/3!+...$
Thus,
$(e^x-1)/x = 1 + x/2!+x^2/3!+...$
Now integrate term-by-term and what do you get?
After I integrate each term, am i done? This is where i get confused in this whole series topic. After i am finished integrating that

x + x^2 / 2*2! + x^4 / 4*3! + ... am i done?

4. Originally Posted by xfyz
After I integrate each term, am i done?
Yes there is no other way to integrate this function. The answer that you got is the anti-derivative just in infinite series form.