We will do this by expanding the integrand as a power series and then integrating term by term.

so:

Hence:

Now we will interchange the order of the integration and summation, which

is valid in this case but I will leave the justification for you to provide:

so:

Summing the first two terms on the right gives an estimate for the integral of 0.0996666667

compared to a fairly accurate numerical integration which gives: 0.0996676643, and the

sum of the first five terms of the series give: 0.0996676643.

RonL