Integrals of the form Type A Problem No 6  Integration  Diploma Maths  2  Summary and Q&A
TL;DR
Learn how to solve the integral ∫dx/(1  sin(2x)  2cos(2x)) using the substitution method.
Key Insights
 🎮 The video explains the stepbystep process of solving a specific integral problem.
 ❓ The substitution method, specifically the tangent substitution, is used to simplify the integral.
 ❓ Finding a common denominator and simplifying fractions are important steps in solving the integral.
Transcript
Read and summarize the transcript of this video on Glasp Reader (beta).
Questions & Answers
Q: What is the integral problem discussed in the video?
The integral problem discussed in the video is ∫dx/(1  sin(2x)  2cos(2x)).
Q: What substitution method is used to solve the integral?
The substitution method used to solve the integral is the tangent substitution (T substitution).
Q: How is the integral simplified after the substitution is made?
After the substitution is made, the integral is simplified by finding a common denominator and simplifying the fractions.
Q: What is the final answer to the integral problem?
The final answer to the integral problem is 1/4 ln3tan(x)  4/3tan(x) + 1 + C.
Summary & Key Takeaways

The video explains how to solve a specific integral problem using the substitution method.

The problem involves finding the integral of 1/(1  sin(2x)  2cos(2x)).

The video demonstrates the stepbystep process of substituting variables and simplifying fractions to solve the integral.