Antiderivatives can be difficult enough to solve on their own, but when you’ve got two functions multiplied together that you need to take the antiderivative of, it can be difficult to know where to start. That’s where the integration by parts formula comes in!

This handy formula can make your calculus homework much easier by helping you find antiderivatives that otherwise would be difficult and time consuming to work out. In this guide, we’ explain the formula, walk you through each step you need to take to integrate by parts, and solve example problems so you can become an integration by parts expert yourself.

Want to dominate your weekly trivia contest? Just looking to expand your knowledge with a variety of random facts? We’ve got you covered! This article contains 113 interesting facts about topics ranging from outer space to history to pop culture. By reading these facts, you’ll learn what camels actually store in their humps, why sunsets on Mars are blue, what crazy use ancient Romans had for human urine, and more. We’ve organized these facts into eight categories. Read all of them or just focus on the specific areas you want to learn more weird facts about!

Struggling with prepositions? These small words can be one of the trickiest parts of speech to understand. However, looking at examples often makes things clearer, which is why we've compiled a list of 49 common preposition examples for you. After recapping what prepositions are, we dive into our list of prepositions, each of which includes a sample sentence. Then we wrap up by giving tips on how to identify different types of prepositions.

Wondering if you have hazel eyes? What are hazel eyes exactly? Although most of us have heard of hazel eyes, many people aren’t quite sure what color they actually are, or if they have hazel eyes themselves. Read this guide for answers to all your hazel eye-related questions, including what the actual hazel eye color is, how someone can get hazel green eyes or hazel brown eyes, how rare hazel eyes are, and how to tell if you have hazel eyes.

What is a compound sentence? How does it differ from a complex sentence? And there are compound-complex sentences, too? Don’t worry, we’ll help you keep them all straight! Read this guide to learn what a compound sentence is, what the different types of compound sentences are, what compound sentence examples look like, and what other sentence types you should know.

Choosing the right ACT test date can significantly impact the score you get. You want to choose a date that gives you both enough time to prepare for the test and enough time to send your scores to schools by their deadlines and potentially retake the ACT if you need to.

At PrepScholar, we constantly review the best data to inform you about future test dates so you can decide well in advance when you want to take the ACT. In this article, we give you the ACT test dates for 2019-2020 and explain the factors to consider in order to select the best test date for you.

You’ve likely heard of the 13 original colonies, but how much do you know about them? When were they created, why were they created, how did they gain their independence, and which states did they become? In this guide, we cover all the important and interesting facts about the 13 colonies, including the official name of each colony, when it was founded, and the role it played up to and during the Revolutionary War. We also give background on the colonies and explain how they eventually became independent states.

Flashcards are an extremely common study tool and, if used correctly, can be one of the most effective ways to learn new information. However, you may not be using them the best way which can reduce how much and how quickly you learn. Want to be an expert flashcard studier? This is your guide! We’ll cover exactly what makes flashcards such a good study tool, where you can make your flashcards, the absolute best method for studying them, and tips to avoid common flashcard pitfalls.

If you’re a teacher, you’re already doing a lot, but luckily there are many tools available to make your job a little bit easier. Teaching tools can help with everything from creating quizzes to promoting good behavior, and many educators find them incredibly useful.

Practically anything can be a teaching tool; a handful of Post-It notes can be a tool if they help you with tasks like figuring out seating arrangements or keeping track of your calendar. However, for the purposes of this guide, we define teaching tools as an online resource that helps teachers with any aspect of their job. Read on to learn what tools for teachers can do and to read descriptions of 17 of the best teaching aids out there.

Looking for games that your toddler will both enjoy and gain important skills from? We’ve got you covered! In this guide, we go over 11 of the best toddler learning games. These educational games for toddlers can be played with few materials, one or more children, and toddlers of varying age ranges. For each game, we explain what skills it will teach toddlers and give instructions on how to set up and play the game.

What’s a googol, and does it have any relation to that similarly-named website? And what about a googolplex, how many zeros does it have? In this guide, we’ll give you googolplex and googol definitions, show how you can write them out, explain how they’re useful, and give examples on how you can start to understand huge numbers like these.

Have you seen images of alchemy symbols and want to know more about what they mean? Alchemy element symbols have been around for centuries, and people are often interested in them because they contain some of the mystique the field of alchemy does.

But what do those symbols mean? And how were the elements they represent used by alchemists? In this guide we’ll give a background on alchemy and alchemy symbols, then we’ll cover every major alchemy symbol, including what it stood for, the properties it was associated with, and any interesting facts that go along with the alchemy symbols and meanings.

Are you studying commensalism in biology class and looking for a good commensalism definition? Commensalism is one of the trickier types of symbiosis to understand, but we'll break it down for you. Read this article to discover what commensalism is, the different types of commensalism, commensalism examples in nature, and the other types of symbiosis and how they differ from commensalism.

What is a vacuole and what does it do? A vacuole is a structure found in animal, plant, bacteria, protist, and fungi cells. It’s one of the largest organelles found in cells, and it’s shaped like a large sac. Vacuoles have a simple structure: they are surrounded by a thin membrane and filled with fluid and any molecules they take in. They look similar to vesicles, another organelle, because both are membrane-bound sacs, but vacuoles are significantly larger than vesicles and are formed when multiple vesicles fuse together.

Confused about transcendentalism? You’re not alone! Transcendentalism is a movement that many people developed over a long period of time, and as a result, its complexity can make it hard to understand.

That’s where we come in. Read this article to learn a simple but complete transcendentalism definition, key transcendentalist beliefs, an overview of the movement's history, key players, and examples of transcendentalist works. By the end, you’ll have all the information you need to write about or discuss the transcendentalist movement.