Solution
= Solution
The <series> for $S$ converges uniformly by the M-test. Therefore <termwise integration> is valid and every term integrates to $\sin(n^3\pi)/n^7=0$, so the <integral> is zero.
= Solution
The <series> for $S$ converges uniformly by the M-test. Therefore <termwise integration> is valid and every term integrates to $\sin(n^3\pi)/n^7=0$, so the <integral> is zero.