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procedure for integration by parts
 1. choose dvmost 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

what do you do if you have a definite integration with IP?
complete IP before FTC









AD
cscxcotxdx=
cscx + C

AD
tanxdx=
lncosx + C


AD
secxdx=
lnsecx + tanx + C

AD
 cscxdx=
lncscx + cotx + C

AD
a^xdx=
 (1/lna)(a^x) + C
 a cannot = 1





AD
1/☑1x^2 dx=
arcsinx + C

AD
1/1+x^2 dx=
arctanx + C

AD
1/x☑x^21 dx=
arcsecx + C

what 2 rules are not for integrals?

lim[f(x) * g(x)]=
lim f(x) * lim g(x)




limit fact
number/0=
+/ infinity

limit fact
number/+/infinity=
0

limit fact
+infinity/number=
+infinity

limit fact
+infinity/+infinity=
L'Hopitals rule

L'Hopital's Rule
Lim f'(x)/g'(x)

limit fact composite
f and g func. that lim g(x)=b and f is cont @b. Then.....
lim f(g(x))=f(b)

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

partial fract decomp
simple linear:
(A/xc1) + (B/xc2).....

part fract decomp
repeated linear
numerator/(xc)^n=

part fract decomp
irreducible quadratic
(Ax+B)/(ax^2+bx+c)

5 steps for partial fraction decomposition
 1. only if numerator is smaller then denominator
 2. completely factor denominator
 3. set og rat func=to part fract decomp
 4. multiply each term by og fact denom
 5. choose x values to eliminate terms and solve

