Logarithmic and Exponential Integrals

What does the acronym LIATE stand for in integration by parts?

• Logarithmic, Inverse trigonometric, Algebraic, Trigonometric, Exponential

• Linear, Integral, Algebraic, Tangential, Exponential

• Logarithmic, Inverse, Arithmetic, Trigonometric, Exponential

• Linear, Inverse, Algebraic, Trigonometric, Exponential

Which of the following is often the first choice for u in the LIATE rule?

• Trigonometric functions

• Logarithmic functions

• Algebraic functions

• Exponential functions

If both logarithmic and inverse trigonometric functions are present, which one is usually chosen as 'u'?

• Logarithmic

• Inverse trigonometric

• Either, depending on the specific integral

• Neither; the rule does not apply in this case

Logarithmic functions are the inverse of...

• Linear Functions

• Exponential Functions 

• Quadratic Functions 

• Polynomial Functions 

• A
• B
• C
• D

• A

• B

• C

• D

Log with a base "e" (log_e) is the same thing as...

• "e"

• Natural Logarithm (LN)

• Common Logarithm (Log)

• Natural Log, base "e"
  LN_e

Log with a base "e" (log_e) is the same thing as...

• "e"

• Natural Logarithm (LN)

• Common Logarithm (Log)

• Natural Log, base "e"
  LN_e

Solve the integral ∫ ln(x) dx.

• x ln(x) - x + C

• ln(x) + C

• x ln(x) + C

• x ln(x) + 1

• A
• B
• C
• D