Learn how to evaluate the integral using rational exponential expression

The video tutorial demonstrates solving an integration problem using substitution. The instructor sets up the problem by letting a variable equal a function of x, then differentiates and integrates to find the solution. The process involves evaluating the integral, considering the absolute value, and simplifying the expression using logarithmic rules. The tutorial concludes with a discussion on finding exact values and using a calculator for verification.

What substitution is used in the problem to simplify the integration process?

• U = e^(x) + 4

• U = e^(x + 4)

• U = ln(x + 4)

• U = x^2 + 4

What is the result of integrating 1/U with respect to U?

• 1/U + C

• ln|U| + C

• U^2/2 + C

• e^U + C

Why is the constant C not needed when using the fundamental theorem of calculus?

• Because C is a variable

• Because C is not part of the integral

• Because C is always zero

• Because C cancels out when subtracting intervals

Why is the absolute value not necessary in the expression ln|e^(x + 4)|?

• Because it is a variable

• Because it is a constant

• Because it simplifies the calculation

• Because e^(x + 4) is always positive

What is the simplified form of ln(e^(ln(3)))?

• ln(3)

• 3

• e^3

• ln(3) + 4

How can the expression ln(7) - ln(13/3) be further simplified?

• ln(3/21)

• ln(21/13)

• ln(7/13)

• ln(13/7)

What is the exact value of the integral after simplification?

• ln(21/13)

• ln(13/21)

• ln(3/7)

• ln(7/3)