How to apply u substitution to find the antiderivative of a rational expression

The video tutorial explains the process of integrating a binomial expression raised to the fifth power using U substitution. It begins by identifying the binomial and setting up the U substitution, followed by differentiating U and setting up the integration problem. The tutorial then demonstrates rewriting the expression with a negative power and integrating it. Finally, it concludes with the integration result and a reminder of the technique used.

What is the first step in recognizing a binomial expression raised to a power?

• Recognize the substitution variable U

• Determine the constant of integration

• Identify the derivative of the expression

• Rewrite the expression in terms of natural logarithms

Why can't the natural logarithm method be used for integrating 1/U^5 DU?

• Because U is not a polynomial

• Because it is not in the form 1/U

• Because the power of U is too high

• Because the derivative of U is not constant

How is the expression 1/U^5 DU rewritten for integration?

• As a constant times U

• As a natural logarithm of U

• As U to the negative 5th

• As U to the power of 5

What is the result of integrating U to the negative 5th?

• U to the negative 4th divided by -4 plus C

• U to the 5th divided by 5 plus C

• U squared divided by 2 plus C

• Natural log of U plus C

What should you remember when encountering a division in integration?

• Always use the natural logarithm method

• Apply the same technique as for multiplication

• Do not get confused by new techniques

• Use a different substitution variable