How do you integrate #f(x)=(-3+3x+3x^2-3x^3)(3-3x-x^2+3x^3+2x^4)# using the product rule?
There is no product rule for integrals - the product rule only applies to derivatives.
In this case, we have to just expand the entire thing:
Combining like terms, we get:
We can then integrate using the reverse power rule, which says:
In our case, we get:
Simplifying, we get: