oblicz calke

[gufox]

\(\displaystyle{ \int sinxsin \frac{x}{2}sin \frac{x}{3}dx}\)

[soku11]

\(\displaystyle{ \sin (x)\cdot \sin ft(\frac{x}{2}\right)\cdot\sin\left(\frac{x}{3}\right)=
\frac{1}{2}\sin (x)\left[ \cos ft(\frac{5}{6}x\right)-\cos ft(\frac{x}{6}\right)\right]=
\frac{1}{2}\sin (x)\cos ft(\frac{5}{6}x\right)-\frac{1}{2}\sin (x)\cos ft(\frac{x}{6}\right)=
\frac{1}{4}\sin ft(\frac{11}{6}x\right)+
\frac{1}{4}\sin ft(\frac{x}{6}\right)-
\frac{1}{4}\sin ft(\frac{7}{6}x\right)-
\frac{1}{4}\sin ft(\frac{x}{6}\right)=
\frac{1}{4}\left[ \sin ft(\frac{11}{6}x\right)-\sin\left(\frac{7}{6}x\right) \right]}\)

Pozdrawiam

[gufox]

takie rzeczy sie liczy z prostego wzoru. dzieki