Integration of Rational Functions Problem No 11 - Integration - Diploma Maths - II

TL;DR

This video discusses a problem on integrating a rational function with multiple steps involved.

Transcript

click the Bell icon to get latest videos from Ekeeda Hello friends in this video we are going to see a last problem on integration of rational functions let us start with problem number 11 integral X raise to 4 upon X square plus 1 DX if you can see again the maximum power of numerator is greater than the denominator therefore we will divide this e... Read More

Key Insights

• 🍉 Integration of rational functions involves dividing the numerator by the denominator and then integrating each term separately.
• ✊ The division is carried out iteratively until the power of the numerator becomes equal to or less than the denominator.
• 👻 Separating the denominator into different terms allows for simpler integration.
• 🍉 Each term in the integral is integrated separately using the appropriate integration rules.
• 😑 Canceling out like terms during the division simplifies the expression.
• 🍉 The final solution is obtained by combining the integrals of each term.
• 🍉 Subtraction of like terms during the division results in cancellation.

Questions & Answers

Q: What is the problem being discussed in the video?

The problem focuses on integrating the rational function X raised to 4 divided by X square plus 1.

Q: How is the division of the numerator and denominator carried out?

The division is done by dividing X raised to 4 by X square, resulting in X square. This process is repeated iteratively until the power of the numerator is no longer greater than the denominator.

Q: How is the final solution obtained?

The final solution is obtained by separating the denominator into two terms and integrating each term individually. This involves integrating X square minus 1, 1, and 1 divided by X square plus 1 separately.

Q: What is the general rule for integrating the given function?

The general rule for integrating the given function is to integrate X square as X cube by 3, integrate 1 as X, and integrate X square plus 1 as inverse X plus C.

Summary & Key Takeaways

• The video presents a problem of integrating a rational function, specifically X raised to 4 divided by X square plus 1.

• It demonstrates the step-by-step division of the numerator by the denominator, canceling out like terms, and simplifying the expression.

• The final solution is obtained by separating the denominator and integrating each term individually.