Basic Integration By Parts

This is a post based on a question.

If it isn't a problem, can I ask you how to integrate by parts?

The properties of integrals let us split up addition, but not multiplication.

So, when we have two functions MULTIPLIED together, we must use the technique of Integration By Parts.

(Note: In this post I will show the formula and explain how to use it, but I will not show why it works. If anyone would like to see where the formula comes from, please let me know in a comment.)

Notice that there is an integral in the answer! This means that to evaluate the problem completely you must also do that integral at the end. This also means that there is potential for the process repeating over and over (you get the answer, but then you have to use Integration By Parts again), but I titled this post Basic Integration By Parts for a reason; repetition would be Advanced Integration By Parts.

Anyway, this formula is critical. After extensive practice, you will know it by heart just because you will use it so much. Before I was entirely familiar with it, however, I had a chant that helped me remember it. All I said was "u v minus v du," but it was enough for me remember it forever.

Now, let's do an example.