Integration by parts is probably the most important technique of
integration after $u$-substitution. Integration by parts works
when your integrand contains a function
multiplied by the derivative of another function.
The formula is
Integration by Parts
$$\int f(x)g'(x) \, dx = f(x)g(x) - \int g(x)f'(x)\, dx.$$
This is cumbersome, so we usually abbreviate by $u=f(x), v=g(x)$ so
that $du=f'(x)\,dx$ and $dv=g'(x)\,dx$. Then our formula
becomes
Integration by Parts
$$\int u \, dv = uv - \int v\, du.$$ You
must learn this formula.
Integration by parts is derived directly from the product rule as you will see in the
video.