  We define and discuss lax and weighted colimits of diagrams in
$\infty$-categories and show that the coCartesian fibration associated to a
functor is given by its lax colimit. A key ingredient, of independent interest,
is a simple characterization of the free Cartesian fibration associated to a a
functor of $\infty$-categories. As an application of these results, we prove
that lax representable functors are preserved under exponentiation, and also
that the total space of a presentable Cartesian fibration between
$\infty$-categories is presentable, generalizing a theorem of Makkai and Par\'e
to the $\infty$-categorical setting. Lastly, in the appendix, we observe that
pseudofunctors between (2,1)-categories give rise to functors between
$\infty$-categories via the Duskin nerve.
