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Use a table of integrals to find the indefinite integral. (Use C for the constant of integration.) 1₁ x13 1 - sec(x¹4) dx

Use a table of integrals to find the indefinite integral. (Use C for the constant of integration.) 1₁ x13 1 - sec(x¹4) dx

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.CR: Chapter 9 Review
Problem 54CR
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### Indefinite Integral Using a Table of Integrals **Problem:** Use a table of integrals to find the indefinite integral. (Use \( C \) for the constant of integration.) \[ \int \frac{x^{13}}{1 - \sec(x^{14})} \, dx \] **Solution:** To solve this integral, refer to the table of integrals typically found in calculus textbooks. The tables provide standard forms and their corresponding integrals, which can simplify the process of integration. Here's how you may approach this: 1. **Identify a Form**: Look for a pattern or form in the given integral that matches one from the table of integrals. 2. **Substitute**: If necessary, perform a substitution to transform the given integral into one of the standard forms. 3. **Integrate**: Use the result from the table of integrals to find the indefinite integral. 4. **Simplify and Include Constant**: Simplify the result and remember to add the constant of integration, \( C \). ### Detailed Explanation of Graphs or Diagrams This problem does not include any graphs or diagrams that require further explanation. It is purely focused on the analytical integration using standard tables. --- This transcription aims to provide clear instructions and guidance for students learning to use integrals tables to solve indefinite integrals.
Transcribed Image Text:### Indefinite Integral Using a Table of Integrals **Problem:** Use a table of integrals to find the indefinite integral. (Use \( C \) for the constant of integration.) \[ \int \frac{x^{13}}{1 - \sec(x^{14})} \, dx \] **Solution:** To solve this integral, refer to the table of integrals typically found in calculus textbooks. The tables provide standard forms and their corresponding integrals, which can simplify the process of integration. Here's how you may approach this: 1. **Identify a Form**: Look for a pattern or form in the given integral that matches one from the table of integrals. 2. **Substitute**: If necessary, perform a substitution to transform the given integral into one of the standard forms. 3. **Integrate**: Use the result from the table of integrals to find the indefinite integral. 4. **Simplify and Include Constant**: Simplify the result and remember to add the constant of integration, \( C \). ### Detailed Explanation of Graphs or Diagrams This problem does not include any graphs or diagrams that require further explanation. It is purely focused on the analytical integration using standard tables. --- This transcription aims to provide clear instructions and guidance for students learning to use integrals tables to solve indefinite integrals.
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