Order when calculating using partial integration

Question

Is the order important when calculating partial integration? When I for example have an integral $$ \int e^x \sin(2x)$$ and the formula for partial integration is $$ \int u v' = u v- \int u' v$$ So when I solve this problem, is the $$e^x \Rightarrow u$$ or is $$sin(2x) \Rightarrow u$$

Answer 1

For this kind of integrals, there is absolutely no difference between the two approaches. You will get the same result. Try by yourself to be convinced

Answer 2

The first function and second function, $u$ and $v$ respectively, are decides by ILATE rule. In $95\%$ it works.

I: Inverse, L:Logarithmic, A: Algebraic, T: Trigonometric and E: Exponential.

We can take Exponential function as the %2nd% function as it is easy to integrate.

In your case, both ways will give the correct answer in equal no of steps.