I know the chain rule for derivatives. The way as I apply it, is to get rid of specific 'bits' of a complex equation in stages, i.e I will derive the $5$th root first in the equation $(2x+3)^5$ and continue with the rest.
I wonder if there is something similar with integration. I tried to integrate that way $(2x+3)^5$ but it doesn't seem to work. Well, it works in the first stage, i.e it's fine to raise in the power of $6$ and divide with $6$ to get rid of the power $5$, but afterwards, if we would apply the chain rule, we should multiply by the integral of $2x+3$!, But it doesn't work like that, we just need to multiply by $1/2$ and that's it.
So my question is, is there chain rule for integrals? I want to be able to calculate integrals of complex equations as easy as I do with chain rule for derivatives.