Math Problem Statement
Integrate number 1-9 using step by step process do not use integration by parts. Box the final answer
Solution
Let's walk through each integration step by step, using the most common methods available, without using integration by parts. We'll box the final answers as you requested.
1.
We start by expressing as a combination of lower powers of sine using the power reduction formula:
Now, we simplify the expression:
Next, expand the product:
Now integrate term by term:
Thus, the final answer is:
2.
Using a similar approach for :
Now expand the product:
After expanding:
Now integrate term by term:
Thus, the final answer is:
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Math Problem Analysis
Mathematical Concepts
Integral Calculus
Trigonometric Integrals
Formulas
Power reduction formula for trigonometric functions
Standard integrals for sin^n(x) and cos^n(x)
Integration of sec^2(x), tan(x), etc.
Theorems
Power Reduction Formula
Basic Integration Techniques
Suitable Grade Level
Grades 11-12
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