6.1 Integration By Parts

Question 1

Integrating by parts is to integration what _________ is to differentiation

Answer 1

Product Rule

Question 2

Formula for Integration by Parts

Answer 2

∫udv = uv - ∫vdu

Question 3

Integration by Parts Steps

Answer 3

1) select a function to serve as u, which will give you a dv
2) differentiate u and integrate dv
3) Plug them into the formula uv - ∫vdu
4) Integrate the final term, repeating if necessary

Question 4

How do you know you’ve selected the proper u function?

Answer 4

1) u is simpler when differentiated
2) dv is easily integratable

Question 5

What do you do when given a single function?

Answer 5

u = function, dv = dx

Question 6

How can you tell when you have a boomerang IBP problem?

Answer 6

exponential function multiplie by trigonometric function

Question 7

Steps of a boomerang Integration by parts problem

Answer 7

1) solve normally via IBP
2) Repeat IBP, which should give you the original integral back as the last term
3) Replace the original integral with L
4) Solve for L