If F is anti derratie for f,

G is antiderivativeto-g ,

fabfg Ifa]! - Ita,ffg : FG

- ffg

ffg = Fg - ff g]

kind

ffsslg :(Hug) - ffllgl

fjh-ffilh-fflilddr.IN

If F is anti derratie fo. f,

Gisantiderintivefo-g.fudv-UV-fvduffda.cat-

- Fa - f. Gdaxff]

If'gdx=fg - ffgidx#

Jj is a family of functions

e.g .Jtc

-

• f X. arc tangent dx

v.f lnlxldx by•f tax) lncxldx

J x are tan Cx)maybe ? I# (rx arc

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hit :÷¥i÷E1-0s,

ffhgdxifg-ffg.ch#J x are tan Cx)-

- f dad'zx¥Iarctanks

-

- t Titan. -si[

IfIx'th) aretancan Ex-⑦ Polynomial x (algebraic)

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an:÷:÷. .:*-

g. fan grant fit②

•- polynomial or rational or algebraic

• inverse trig or log ③

• trig & et①

dammit : '

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the right w/ i Bp"

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f%tcxDgi dx=

ffxiglxl-ffaadffglxddxflncxldxfh.itaxs) In dx

=

If'I,t=x3txs

f! thand. ¥a⇒

÷÷i*÷¥= i.

'ftp.lnaa-ffytxfteddx÷¥iElnx-s¥iEH

fltn (x) dy = fda,fIf . In addx

+N xd d

= xlnext - fx HuixD d.x+d - - -

= xlnext - fi de= x Incx) - X

te

d⇐ feta x

-x]

In x t l- I = In X