Integral of sin(2x)cos(2x)  Summary and Q&A
TL;DR
This content explains how to integrate the product of sine and cosine using a substitution method.
Key Insights
 💨 There are multiple ways to integrate sine(2x) * cosine(2x), including using trigonometric identities and substitutions.
 💦 Letting u be equal to sine(2x) simplifies the integration process significantly.
 🎅 The final solution is (1/4) * sin^2(2x) + C, where C represents the constant of integration.
Transcript
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Questions & Answers
Q: What are the different approaches to integrating sine(2x) * cosine(2x)?
The video mentions that possible approaches include using a trigonometric identity, making a usubstitution, or choosing u as sine or cosine. However, letting u be equal to sine(2x) is the most straightforward approach.
Q: How does the derivative of sine(2x) relate to the substitution method?
The derivative of sine(2x) involves the cosine function, making it a suitable substitution. This choice simplifies the integration process.
Q: What does the substitution transform sine(2x) * cosine(2x) into?
After making the substitution, the integration becomes (1/2) * du, where u represents sine(2x).
Q: How do we find the final solution after making the substitution?
By integrating (1/2) * du, we apply the power rule to obtain (1/4) * sin^2(2x) + C, where C is the constant of integration.
Summary & Key Takeaways

The video discusses different approaches to integrate sine(2x) * cosine(2x).

The best approach is to let u be equal to sine(2x) and use the derivative chain rule.

After making the substitution, the integration simplifies to (1/4) * sin^2(2x) + C.