Integrating by Substitution and Parts (6.1-6.2) Flashcards
Anti dx of sinx
-cosx + c
anti dx of cosx
sinx + c
anti dx of tanx
-ln |cosx| + c
anti of cscx
-ln |cscx + cotx| + c
anti dx of secx
ln |secx + tanx| + c
anti dx of cotx
ln |sinx| + c
anti dx of 1/a^2 + x^2
1/a times arctan x/a + c
anti dx of 1/square root of a^2 + x^2
arcsin of x/a + c
anti dx of 1/x times the square root of x^2 - a^2
1/a sec^-1 of x/a + c
How to complete square
a^2 -b/2 ^2 + b/2 ^2 + c
Simple steps for u-sub
pick a u
find du
plug in du
integrate
plug u
evaluate if there are bounds
In a fraction your u should be the….
Bottom
Integration by parts theorem
integral of u dv = uv - integral of vdu
How do you choose a u and v
U L I A T E V
Simple integration by parts steps
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
What is the point of integration by parts
You want an easier function to integrate
When you integrate again and get the same equation as question you have….and what to do
a relationship
-set the question equal to your work and solve for the integral
when should you use u-sub vs integrating by parts
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
What do you when you have u-sub but you do it and you have a variable not u left over
solve for it with the u = x stuff you found
derivative of sin ^-1
1 / square root of 1 - x^2
derivative of cos^-1
-1/ square root of 1 - x^2
derivative of tan^-1
1/ 1 + x^2
