Math Problem Statement
Solution
It looks like you've shared a page from a mathematics textbook containing integral formulas, with several items marked with blue checks. If you'd like, I can:
- Verify or explain any specific formula listed.
- Solve an example integral related to one of these formulas.
- Discuss techniques for solving integrals like these.
- Clarify any part of the notation or the steps involved in deriving these formulas.
Let me know how you'd like to proceed!
5 Follow-Up Questions
- Would you like me to explain the derivation of one of these formulas?
- Do you need help solving an integral similar to one of these?
- Would you like me to simplify or rewrite one of these expressions for clarity?
- Should I discuss the applications of these fundamental integration formulas?
- Do you want tips on how to recognize when to use these formulas in practice?
Tip
Practice matching integrals to their corresponding formula—it will help you solve problems faster during exams or assignments!
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Math Problem Analysis
Mathematical Concepts
Integration
Indefinite Integrals
Fundamental Integration Formulas
Formulas
∫(√x - 1)dx = (2/3)x^(3/2) - x^(1/2) + C
∫dx/√(x + 3) = 2√(x + 3) + C
∫√(2 - 3x) dx = -(1/2)(2 - 3x)^(3/2) + C
∫(e^(x) + 1)^2 dx = e^(2x) + 2e^(x) + x + C
Theorems
Fundamental Theorem of Calculus
Power Rule for Integration
Suitable Grade Level
Grades 11-12, Undergraduate Calculus
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