Question

find power series (maclaurin series):
integral [ cos(x^3) ] dx

Answer 1

Where you stuck at?

Answer 2

can you take me through it from the top?

Answer 3

Maclaurin series is: \[
f(x) = \sum_{n=0}^\infty f^{(n)}(0)\frac{x^n}{n!}
\]

Answer 4

All you really need to find is the patter for the derivative at \(0\).

Answer 5

Our function in this case is: \[
f(x) = \int \cos(x^3)~dx
\]Is this correct?

Answer 6

I believe all we have to do is take the Maclaurin series of the integrand and integrate it, then do a bit of simplification.

Answer 7

But really, where are you stuck?