[tex]\displaystyle\int\cos^56x\sin6x\,\mathrm dx[/tex]
Let [tex]y=\cos6x[/tex], so that [tex]\mathrm dy=-6\sin6x\,\mathrm dx[/tex]. Then
[tex]\displaystyle\int\cos^56x\sin6x\,\mathrm dx=-\frac16\int y^5\,\mathrm dy=-\frac1{36}y^6+C=-\frac1{36}\cos^66x+C[/tex]
