# Calc II chap 8

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1. procedure for integration by parts
• 1. choose dv-most difficult part that can use basic or substitution
• 2. rest is u
• 3. differentiate u to get du
• 4. substitute into IP formula uv - |vdu
• 5. integrate to finish
2. what do you do if you have a definite integration with IP?
complete IP before FTC
3. formula for IP
uv-|vdu
|kdx=
kx + C
|k f(x)dx=
k |f(x)
|cosxdx=
sinx + C
|sinxdx
-cosx + C
|sec^2xdx=
tanx + C
|csc^2xdx=
-cotx +C
|secxtanxdx=
secx + C
|cscxcotxdx=
-cscx + C
|tanxdx=
-ln|cosx| + C
|cotxdx=
ln|sinx| + C
|secxdx=
ln|secx + tanx| + C
| cscxdx=
-ln|cscx + cotx| + C
a^xdx=
• (1/lna)(a^x) + C
• a cannot = 1
e^xdx=
e^x + C
lnxdx=
xlnx - x + C
1/xdx=
ln|x| + C
x^-1dx
ln|x| + C
1/☑1-x^2 dx=
arcsinx + C
1/1+x^2 dx=
arctanx + C
1/x☑x^2-1 dx=
arcsec|x| + C
24. what 2 rules are not for integrals?
• product
• quotient
25. lim[f(x) * g(x)]=
lim f(x) * lim g(x)
26. lim c=
c
27. lim x =
a
28. lim x^n =
a^n
29. limit fact
number/0=
+/- infinity
30. limit fact
number/+/-infinity=
0
31. limit fact
+-infinity/number=
+-infinity
32. limit fact
+-infinity/+-infinity=
L'Hopitals rule
33. L'Hopital's Rule
Lim f'(x)/g'(x)
34. limit fact composite
f and g func. that lim g(x)=b and f is cont @b. Then.....
lim f(g(x))=f(b)
35. limit fact squeeze theorem
f(x)◀g(x)◀h(x) on interval w/a
if lim f(x)=L and lim h(x)=L, then...
lim g(x)=L
36. partial fract decomp
simple linear:
(A/x-c1) + (B/x-c2).....
37. part fract decomp
repeated linear
numerator/(x-c)^n=
38. part fract decomp