Answer:

General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Calculus</u>
Derivatives
Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Antiderivatives - Integrals
Indefinite Integrals
U-Substitution
Integration Property [Multiplied Constant]: 
Arctrig Integration [arctangent]: 
Step-by-step explanation:
<u>Step 1: Define</u>

<u>Step 2: Integrate Pt. 1</u>
- [Integral] Rewrite:

<u>Step 3: Identify Variables</u>
<em>Identify variables for u-substitution of arctrig.</em>
- Set <em>u</em>:

- Differentiate [Basic Power Rule]:

- [Derivative] Simplify:

- [Derivative] Rewrite:

- Set <em>a</em>:

<u>Step 4: Integrate Pt. 2</u>
- [Integral] Rewrite [Integration Property - Multiplied Constant]:

- [Integral] U-Substitution:

- [Integral] Arctrig Integration [arctangent]:
![\displaystyle \frac{1}{2}[\frac{1}{a}arctan(\frac{u}{a})] + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B2%7D%5B%5Cfrac%7B1%7D%7Ba%7Darctan%28%5Cfrac%7Bu%7D%7Ba%7D%29%5D%20%2B%20C)
- [Integral] Back-Substitute:
![\displaystyle \frac{1}{2}[\frac{1}{1}arctan(\frac{2x}{1})] + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B2%7D%5B%5Cfrac%7B1%7D%7B1%7Darctan%28%5Cfrac%7B2x%7D%7B1%7D%29%5D%20%2B%20C)
- [Integral] Divide:
![\displaystyle \frac{1}{2}[arctan(2x)] + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B2%7D%5Barctan%282x%29%5D%20%2B%20C)
- [Integral] Multiply:

Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration of Arctrig
Book: College Calculus 10e