Hello, I'm having trouble with the question below. I'm supposed to use a power series to approximate this integral, but the way I tried it seemed to fail horribly. Does anybody know how to do this?

Use a power series to approximate the definite integral to six decimal places.

What I tried was to take the derivative, then make a power series for that, and then integrate that summation twice. That's most likely wrong, but I'm not sure why. Any help would be appreciated.

Thank you