Evaluate the indefinite integral as an infinite series

• May 4th 2010, 03:52 PM
CalculusCrazed
Evaluate the indefinite integral as an infinite series
I am having some trouble with:

integral of $xcos(x^3)$

any ideas?
• May 4th 2010, 03:57 PM
skeeter
Quote:

Originally Posted by CalculusCrazed
I am having some trouble with:

integral of $xcos(x^3)$

any ideas?

$\cos{x} = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + ...$

$\cos(x^3) = 1 - \frac{x^6}{2!} + \frac{x^{12}}{4!} - \frac{x^{18}}{6!} + ...$

$x\cos(x^3) = x - \frac{x^7}{2!} + \frac{x^{13}}{4!} - \frac{x^{19}}{6!} + ...$

integrate it, term for term ...