Integration without integration

There is a special integration “formula” that you can use to integrate products of Physics and engineering functions:

eax              sin bx                  cos cx
,where a, b and c are constants.

$$\int f \, g = \frac{f\, g^{\prime}-f^{\prime}\, g}{u-v} + C$$

, where $f^{\prime \prime} = vf$ and $g^{\prime \prime} = ug$, $u \neq v$

Note that if u = v, this formula cannot be used. (It hardly happens)

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