Question

$$\int \sin^{2}\frac{x}{4}\cos^{2}\frac{x}{4}dx;$$

Answer

$$int*sin(4*cos*x)^2*(4*x^2*d)^2;$$

Solution


Regroup terms.
\[\begin{aligned}&int\sin^{2}(4cosx){(x\times 4dx)}^{2}\\&\end{aligned}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\begin{aligned}&int\sin^{2}(4cosx){({x}^{2}\times 4d)}^{2}\\&\end{aligned}\]
Regroup terms.
\[\begin{aligned}&int\sin^{2}(4cosx){(4{x}^{2}d)}^{2}\\&\end{aligned}\]