Question

Evaluate the integral as a series.
\[\int xcos(x^3)dx\]
\[cosx=\sum_{n=0}^{\infty}(-1)^n\frac{x^{2n}}{(2n)!}\]
sooooo.....
\[=\int\sum_{n=0}^{\infty}(-1)^n\frac{x^{6n+1}}{(2n)!}\]
Yes?

Answer 1

yup, now just integrate.

Answer 2

\[\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n)!}\frac{x^{6n+2}}{6n+2}\]

Answer 3

Awww thank you!