How to solve this problem using integration?
\(\displaystyle\int\cos^56x\sin6x\,\mathrm dx\)Let \(y=\cos6x\), so that \(\mathrm dy=-6\sin6x\,\mathrm dx\). Then\(\displaystyle\int\cos^56x\sin6x\,\mathrm dx=-\frac16\int y^5\,\mathrm dy=-\frac1{36}y^6+C=-\frac1{36}\cos^66x+C\)
