The curve isCparametrized by $\displaystyle \vec{r}(t) = (t^4cos^2(2\pi e^t),t^4sin^2(2\pi e^t)) $, where $\displaystyle 0 \leq t \leq \pi /4$. We also have $\displaystyle \vec{F} (x,y) = (y,x)$

Calculate the line integral: $\displaystyle \int_C \vec{F}* d\vec{r}$

I find that I have to solve the integral:

$\displaystyle \int_0^{\pi/4} {(8t^7cos(t)sin(t) + t^8(cos^2(t)-sin^2(t))) dt}$

How can I solve this integral quickly?