Exercise
$\int\sin^4\left(\frac{x}{3}\right)cos^4\left(\frac{x}{3}\right)dx$
Step-by-step Solution
Final answer to the exercise
$\frac{-3\sin\left(\frac{x}{3}\right)^{3}\cos\left(\frac{x}{3}\right)^{5}}{8}-\frac{45}{256}\sin\left(\frac{2x}{3}\right)-\frac{15}{128}x+\frac{-15\cos\left(\frac{x}{3}\right)^{3}\sin\left(\frac{x}{3}\right)}{64}-\frac{3}{16}\cos\left(\frac{x}{3}\right)^{5}\sin\left(\frac{x}{3}\right)+\frac{27}{128}\sin\left(\frac{2x}{3}\right)+\frac{9}{64}x+\frac{9\cos\left(\frac{x}{3}\right)^{3}\sin\left(\frac{x}{3}\right)}{32}+C_0$