Is there really no analogue of the derivative product rule for integrals, or we just haven't found one yet?

I thought there was already such a question here, but I did not find it.

As the comments say, there is no simple formula for $\int f g dx$ in terms of $\int f dx$ and $\int g dx$. There are lots of ways to see this.

(A) $$ \int x\;dx\quad\text{and}\quad \int\frac{1}{x^2}\;dx\quad \text{are rational functions, but}\quad \int\frac{1}{x}\;dx\quad\text{is not} . $$ (B) $$ \int x e^{x^2}\;dx\quad\text{and}\quad \int\frac{1}{x}\;dx\quad \text{are elementary functions, but}\quad\int e^{x^2}\;dx\quad\text{is not} . $$ You come up with what "simple formula" means, then there should be an example like these using that notion of "simple formula".

Tags:

Integration

Calculus

Products

Closed Form

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