Calculus – Evaluate $\int \cos(3x) \sin(2x) \, dx$

Question

Evaluate the indefinite integral
\begin{align}
\int \cos(3x) \sin(2x) \, dx
\end{align}

Please see my work attempt as my answer below.

Answer 1

HINT:

Using Werner Formulas

$$2\cos3x\sin2x=\sin(3x+2x)-\sin(3x-2x)$$

Now use $\displaystyle\int\sin mx\ dx=-\frac{\cos mx}m+C$

Finally and optionally, we can use Multiple Angle Formula to expand $\cos5x$ in the power of $\cos x$