Answer:
General Formulas and Concepts:
Algebra I
- Terms/Coefficients
- Factoring
Algebra II
Calculus
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
Explanation:
*Note:
You could use u-solve instead of rewriting the integrand to integrate this integral.
Step 1: Define
Identify
Step 2: Integrate Pt. 1
- [Integrand] Rewrite [Polynomial Long Division (See Attachment)]:
- [Integral] Rewrite [Integration Property - Addition/Subtraction]:
- [Integrals] Rewrite [Integration Property - Multiplied Constant]:
- [1st Integral] Reverse Power Rule:
Step 3: Integrate Pt. 2
Identify variables for u-substitution.
- Set u:
- [u] Differentiate [Basic Power Rule]:
Step 4: Integrate Pt. 3
- [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