$(25$ points$)$ Compute the following integrals

$($a$){\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}co{s}^4(4x)dx$

$($b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}ta{n}^{4}xse{c}^{6}xdx$

Solve all questions with detailed step by step format, and all the formulas and why that specific formula is used for the problem.