Integration by Parts

Guidelines for selecting u and dv:

  • Remember “L-I-A-T-E” where you choose “u” to be the function that comes first in the list.

    1. L - Logrithmic Function
    2. I - Inverse Trig Function
    3. A - Algebraic Function
    4. T - Trig Function
    5. E - Exponential Function
    • Example: Integration by Parts Example 1
  • Alternative Guidelines for Choosing u and dv:

    1. dv is the complicated portion of the integrand that can easily be integrated.
    2. u is the integrand whose derivative du is a “simpler” function than u itself.
    • Example: Integration by Parts Example 2
  • Repeated Applications of Integration by Parts: Integration by Parts Example 3

Trig Formulas to Memorize

Trig Integrals

Trig Identities

  1. Defining relations for tangent, cotangent, secoant, and cosecant in terms of sine and cosine. Defining Relations
  2. Pythagorean formula for sines and cosines. Pythagorean
  3. Identities expressing trig functions in terms of their complements. Identities expressing trig functions
  4. Periodicity of trig functions.

NOTE: Sine, cosine, secant, and cosecant have period 2pi while tangent and cotangent have period pi. Periodicity of trig functions

  1. Identites for negative angles.

NOTE: Sine, tangent, cotangent, and cosecant are odd functions while cosine and secant are even functions. Identities for negative angles

  1. Ptolemy’s identities, the sum and difference formulas for sine and cosine. Ptolemy’s identities, the sum and difference formulas for sine and cosine.
  2. Double angle formlas for sine and cosine

NOTE: There are three forms for double angle formula for sine. Double angle formlas for sine Double angle formlas for cosine