Question

найти интеграл sin x/3 cos x/3 dx

Answer 1

$\int \sin \frac x 3 \cos \frac x 3 dx=\int \frac{\sin \frac{2x}{3}}{2}dx=\frac12\int (\frac32*\sin\frac{2x}{3} d(\frac{2x}{3}))=\frac34*(-\cos \frac{2x}{3})+C\\ =-\frac34 \cos \frac {2x}{3}+C$