Answer:

General Formulas and Concepts:
Calculus
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
![\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)](https://img.qammunity.org/2021/formulas/mathematics/college/bz16ipe6p14y3f6abzxt2zy0j41tg530u9.png)
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]:
![\displaystyle (d)/(dx)[f(g(x))] =f'(g(x)) \cdot g'(x)](https://img.qammunity.org/2021/formulas/mathematics/college/ljowxevzhh8dk8mfdheam579ywk5jvteyi.png)
Integration
Integration Rule [Reverse Power Rule]:

Integration Rule [Fundamental Theorem of Calculus 1]:

Integration Property [Multiplied Constant]:

Integration by Parts:

- [IBP] LIPET: Logs, inverses, Polynomials, Exponentials, Trig
Explanation:
Step 1: Define
Identify

Step 2: Integrate Pt. 1
Identify variables for integration by parts using LIPET.
- Set u:

- [u] Logarithmic Differentiation [Derivative Rule - Chain Rule]:

- [du] Basic Power Rule [Derivative Property - Multiplied Constant]:

- [du] Simplify:

- Set dv:

- [dv] Integration Rule [Reverse Power Rule]:

Step 3: Integrate Pt. 2
- [Integral] Integration by Parts:

- [Integral] Rewrite [Integration Property - Multiplied Constant]:

- [Integral] Integration Rule [Reverse Power Rule]:

- Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration