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**wingless** Yes, it's easier to integrate it but it won't bring you anywhere. But if we differentiate x, it'll be 1 and if we differentiate 1, we get 0. This means you will surely get a result using integration by parts 2 times. Learn tabular integration, it makes easier to use multiple partial integrations.

If you have troubles integrating this, you can substitute $\displaystyle u=2x$ before starting.

$\displaystyle \int x \cos 2x ~dx$

$\displaystyle u=2x$

$\displaystyle du = 2dx$

$\displaystyle x=\frac{u}{2}$

So it becomes $\displaystyle \frac{1}{4} \int u \cos u ~du$ which is easier to integrate.