Integrating by Substitution and Parts (6.1-6.2)

Question 1

Anti dx of sinx

Answer 1

-cosx + c

Question 2

anti dx of cosx

Answer 2

sinx + c

Question 3

anti dx of tanx

Answer 3

-ln |cosx| + c

Question 4

anti of cscx

Answer 4

-ln |cscx + cotx| + c

Question 5

anti dx of secx

Answer 5

ln |secx + tanx| + c

Question 6

anti dx of cotx

Answer 6

ln |sinx| + c

Question 7

anti dx of 1/a^2 + x^2

Answer 7

1/a times arctan x/a + c

Question 8

anti dx of 1/square root of a^2 + x^2

Answer 8

arcsin of x/a + c

Question 9

anti dx of 1/x times the square root of x^2 - a^2

Answer 9

1/a sec^-1 of x/a + c

Question 10

How to complete square

Answer 10

a^2 -b/2 ^2 + b/2 ^2 + c

Question 11

Simple steps for u-sub

Answer 11

pick a u
find du
plug in du
integrate
plug u
evaluate if there are bounds

Question 12

In a fraction your u should be the….

Answer 12

Bottom

Question 13

Integration by parts theorem

Answer 13

integral of u dv = uv - integral of vdu

Question 14

How do you choose a u and v

Answer 14

U L I A T E V

Question 15

Simple integration by parts steps

Answer 15

choose u
choose dv
take derivative of u and integrate dv
plug into theorem equation

OR TABULAR METHOD
-Make a chart of derivative vs integral, keep going until a 0 of derivative
-use diagonal red arrow (multiplying) for adding or subtracting the product (start with + and switch off)
-use blue horizontal line for integration

Question 16

What is the point of integration by parts

Answer 16

You want an easier function to integrate

Question 17

When you integrate again and get the same equation as question you have….and what to do

Answer 17

a relationship
-set the question equal to your work and solve for the integral

Question 18

when should you use u-sub vs integrating by parts

Answer 18

u-sub when you see a derivative of a part

by parts when you see the terms being multiplied and dont see a derivative part

Question 19

What do you when you have u-sub but you do it and you have a variable not u left over

Answer 19

solve for it with the u = x stuff you found

Question 20

derivative of sin ^-1

Answer 20

1 / square root of 1 - x^2

Question 21

derivative of cos^-1

Answer 21

-1/ square root of 1 - x^2

Question 22

derivative of tan^-1

Answer 22

1/ 1 + x^2