Evaluate   \( \int_{0}^{1}\ 5x(4x^2+1)^3 \)

\begin{align} \int_{0}^{1} 5x(4x^2+1)^3 & = \left[ \frac{5}{32}(4x^2+1)^4 \right]_{0}^{1} \\ \\ & = \left(\frac{5}{32}(4(1^2)+1)^4 \right)- \left(\frac{5}{32}(4(0^2)+1)^4 \right) \\ \\ & = \frac{3125}{32}- \frac{5}{32} \\ \\ & = \frac{3120}{32} \\ \\ & = 97 \frac{1}{2} \end{align}