How can I find the indefinite integral of $\int\sin^3x \cos^3x dx $? I am looking to evaluate the indefinite integral
\begin{equation*}
\int\sin^3x \cos^3x dx. 
\end{equation*}
I'm not sure if I started this right but I broke the terms up like this:
\begin{equation*}
\int\sin^2x \sin x \cos^2x \cos x 
\end{equation*}
Edit: I got 
\begin{equation*}
{1 \over 4}\cos^4x + {1 \over 6}\cos^6x + C 
\end{equation*}
but my book says it should be sine not cosine

Let's "linearise" the integrand
$$\begin{align}\sin^3{x}\cos^3{x}&=\left(\frac{\sin{2x}}{2}\right)^3\\
&=\frac{1}{8}\left(\frac{e^{2ix}-e^{-2ix}}{2i}\right)^3\\
&=\frac{1}{8}\frac{e^{6ix}-3e^{2ix}+3e^{-2ix}-e^{-6ix}}{-8i}\\
&=\frac{-\sin{6x}+3\sin{2x}}{32}\end{align}$$
And it boils down to integrating two sines.
