Answer :
From the calculation, u is represented as x⁷ and dv as e^10xdx
The formula for calculating integration by part is expressed as:
Given [tex]\int\limits f(x)g(x) \, dx[/tex]
Let u = f(x) and dv = g(x)dx, according to integration by part:
[tex]\int\limits u \, dv = uv - \int\limits v \, du[/tex]
Comparing the general formula above to the given integral function [tex]\int\limits x^7e^{10x} \, dx[/tex]
f(x) = x⁷ and g(x) = e^10x
Comparing this with the formula [tex]\int\limit {u} \, dv[/tex]
u = x⁷ and dv = e^10xdx
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Answer:
[tex]\displaystyle u = x^7[/tex]
[tex]\displaystyle du = e^{10x} \ dx[/tex]
General Formulas and Concepts:
Calculus
Integration
- Integrals
Integration by Parts: [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]
- [IBP] LIPET: Logs, inverses, Polynomials, Exponentials, Trig
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {x^7e^{10x}} \, dx[/tex]
Step 2: Integrate Pt. 1
Identify variables for integration by parts using LIPET.
- Set u: [tex]\displaystyle u = x^7[/tex]
- Set dv: [tex]\displaystyle du = e^{10x} \ dx[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration