If you want to use integration by parts to find u = (x + 9)? Explain your choice then integrate. Choose the correct answer below. A. The better choice is u = (x + 1) √(x + 1)²(x + 9) dx, which is the better choice for u: u = ... because it contains a quantity to a power. B. The better choice is u = (x + 1) because it is easier to integrate e fu dv. C. The better choice is u = (x + 9) because it is next to dx in the integrand. Sudv. √(x + 1)²(x+9) dx = D. The better choice is u = (x + 9) because it is easier to integrate u = (x + 1)² or
If you want to use integration by parts to find u = (x + 9)? Explain your choice then integrate. Choose the correct answer below. A. The better choice is u = (x + 1) √(x + 1)²(x + 9) dx, which is the better choice for u: u = ... because it contains a quantity to a power. B. The better choice is u = (x + 1) because it is easier to integrate e fu dv. C. The better choice is u = (x + 9) because it is next to dx in the integrand. Sudv. √(x + 1)²(x+9) dx = D. The better choice is u = (x + 9) because it is easier to integrate u = (x + 1)² or
Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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### Integration by Parts Choice
**Question:**
If you want to use integration by parts to find \(\int (x + 1)^7 (x + 9) \, dx\), which is the better choice for \(u\): \(u = (x + 1)^7\) or \(u = (x + 9)\)? Explain your choice then integrate.
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### Answer Choices:
**Choose the correct answer below.**
**A.** The better choice is \(u = (x + 1)^7\) because it contains a quantity to a power.
**B.** The better choice is \(u = (x + 1)^7\) because it is easier to integrate \(\int u \, dv\).
**C.** The better choice is \(u = (x + 9)\) because it is next to \(dx\) in the integrand.
**D.** The better choice is \(u = (x + 9)\) because it is easier to integrate \(\int u \, dv\).
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\[ \int (x + 1)^7 (x + 9) \, dx = \quad \boxed{\phantom{answer}} \]
### Solution Explanation:
- **Integration by parts formula:**
\[ \int u \, dv = uv - \int v \, du \]
- Choose \(u\) such that \(du\) simplifies the integration.
- Choose \(dv\) such that \(v\) is easy to find.
Compare the choices:
- \(u = (x + 1)^7\) results in complex \(du\).
- \(u = (x + 9)\) results in simpler \(du = dx\).
Hence, **D** is the correct choice: \(u = (x + 9)\) because it is easier to integrate \(\int u \, dv\).
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b1cab43-2155-41da-a401-15f3493c67ce%2Fe92042a8-90c5-4cdb-a9d6-b03a9400d69f%2Feonvylr_processed.png&w=3840&q=75)
Transcribed Image Text:---
### Integration by Parts Choice
**Question:**
If you want to use integration by parts to find \(\int (x + 1)^7 (x + 9) \, dx\), which is the better choice for \(u\): \(u = (x + 1)^7\) or \(u = (x + 9)\)? Explain your choice then integrate.
---
### Answer Choices:
**Choose the correct answer below.**
**A.** The better choice is \(u = (x + 1)^7\) because it contains a quantity to a power.
**B.** The better choice is \(u = (x + 1)^7\) because it is easier to integrate \(\int u \, dv\).
**C.** The better choice is \(u = (x + 9)\) because it is next to \(dx\) in the integrand.
**D.** The better choice is \(u = (x + 9)\) because it is easier to integrate \(\int u \, dv\).
---
----------
\[ \int (x + 1)^7 (x + 9) \, dx = \quad \boxed{\phantom{answer}} \]
### Solution Explanation:
- **Integration by parts formula:**
\[ \int u \, dv = uv - \int v \, du \]
- Choose \(u\) such that \(du\) simplifies the integration.
- Choose \(dv\) such that \(v\) is easy to find.
Compare the choices:
- \(u = (x + 1)^7\) results in complex \(du\).
- \(u = (x + 9)\) results in simpler \(du = dx\).
Hence, **D** is the correct choice: \(u = (x + 9)\) because it is easier to integrate \(\int u \, dv\).
---
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