Answer:
General Formulas and Concepts:
<u>Algebra I</u>
- Terms/Coefficients
- Factoring
<u>Algebra II</u>
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
Derivative Property [Addition/Subtraction]:
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Integration
- Integrals
- Integration Constant C
- Indefinite Integrals
Integration Rule [Reverse Power Rule]:
Integration Property [Multiplied Constant]:
Integration Property [Addition/Subtraction]:
Logarithmic Integration
U-Substitution
Step-by-step explanation:
*Note:
You could use u-solve instead of rewriting the integrand to integrate this integral.
<u>Step 1: Define</u>
<em>Identify</em>
<u>Step 2: Integrate Pt. 1</u>
- [Integrand] Rewrite [Polynomial Long Division (See Attachment)]:
- [Integral] Rewrite [Integration Property - Addition/Subtraction]:
- [Integrals] Rewrite [Integration Property - Multiplied Constant]:
- [1st Integral] Reverse Power Rule:
<u>Step 3: Integrate Pt. 2</u>
<em>Identify variables for u-substitution.</em>
- Set <em>u</em>:
- [<em>u</em>] Differentiate [Basic Power Rule]:
<u>Step 4: Integrate Pt. 3</u>
- [Integral] Rewrite [Integration Property - Multiplied Constant]:
- [Integral] U-Substitution:
- [Integral] Logarithmic Integration:
- Back-Substitute:
- Factor:
- Rewrite:
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e