TITLE: Separating integrals to solve difficult problems
QUESTION [0 upvotes]: If I have the integral of f(x)g(x) by dx can I do the integrals separately and multiply the products together ? i.e is it true that 
$$\int f(x)g(x)  dx=(\int f(x) dx).(\int g(x)dx)?$$

REPLY [1 votes]: No, let $f(x)=g(x)=x$, so that
$$\int x^2 dx= \frac{x^3}3\neq (\frac{x^2}2)(\frac{x^2}2)= (\int x dx)(\int x dx)$$
{"set_name": "stack_exchange", "score": 0, "question_id": 1740652}