Integration by partsThe Formula:

∫𝑢𝑑𝑣=𝑢 ∙𝑣−∫𝑣 𝑑𝑢Ultra Violet Voo Doo

The Idea: To express the original integral in terms of a second integral that you know how to integrate.

Use this formula for expressions that you don’t know how to integrate like

I L A T E - What is u? dv? Inverse Trig Logarithmic Logarithmic (and Algebraic) Algebraic (and Exponential) Algebraic (and Trigonometric) Trigonometric (and exponential)

Agenda: Feb. 6• 7.2 Integration by Parts – part deux• HW questions• An unusual solution – requires solving

the solution for the solution – huh?• Tabular method – a shortcut

ILATE is a guideline, doesn’t always tell you what to pick for u. Choose that you know how to integrate. Trial and Error method.

– a shortcut. Works well for problems with

Homework

p. 494 #18, 19, 22, 36, 43, Tabular: 59-63 (odd) , 77, 99, 106

Not all will require IBP, some may be substitution!

1. Solve the initial value problem : ;

Continue working on Challenge problems

Homework: