to accompany Stewart's Calculus
General Formulas
l. Lc=odx
t. fiff f*>+g(x)l = .f'(x)+s'(x)s. fttf O>s(x)l =
f'(x)g(x)+ f(x)g'(x) (Product Rule),. + lry) _ s@)f (x)- f !x)s'@)
(euotient Rule)e ls?).] [g(")]'z. ftrer'>) = /'(g(x))g'(x)8. Lf
=nx'-ldxExponential and Logarithmic Functions
9. d e'-e'dx
t. Lnl1 =1dx rr xTrigo no metric F unctio ns
B. lsinx: cosxdx
rc. Lcsc.r:-csc x cotxdx
I nverse Trigonometric Functions
19.4sin-'x=-:Ldx "!l- *'
22. Lcsc-tdx *J r' -l
Hyperbolic Functions
25. Lsinhx= cosh.rdx
28. L csch x= -
csch xcoth xdx
I nverse Hyp erb olic F uictio ns
31.4sinh-'dx ^h+ *'
23.4sec-'dx *J *' -l
Dffirentiation Rules
M. lcosx:-sinxdx
n. Lsec x : sec.r tan.xdx
20. 4cos-,x - ---!-dx Jt- *'
26. lcoshx= sinh.rdx
29. ! sech x= -
sech x tanh xdx
32. Lcosh-'" =-!dx ,l*' -t
35. 4sech-'dx ,Jt - ,'
z. ftt"roll= cf'(x)
e. ftttol -g(r)l = f' (x) - g'(x)
(Chain Rule)
(Power Rule)
t0. La' = ar lnadx
n.LrcBr= Idx xlna
E. ltanx: sec'.rdx
fi. lcotr:-csc',dx
2t.Ltant*= | =dx l+x"
24. Lcot-', = --L-dx l+x'
zl. ltanhx= sech2 xdx
30. lcothx= -csch2 xdx
:s.4tanh-'r=-f-dx l-x'36. 4coth-'*=ldx l- x'M. !csch-'x=--!dx
lrlJ", +r
Basic Formalas
t. I*'d*=fi+c @+-r)3,;l ;dr=1tun-' "+crx-+a- a aTrigo no m etric
F unctio n sS. Jsinx dx=-cosx+C7. Jsect xdx=tanx+C9. Jsecxtanx
dx=secx+C11. Jtanx ah = hlsecxl+ C
13. Jsecx dr = hlsecx+ tanrl+ C
15. fsin'? , a*=!*-Lsin2x+Cr2417. fsin'x dx=-!sin'-' r.or"*n-l
lsin'-2xdxJnnJExponential and Logarithmic Functions
19. [e'dx=e'+C21. !e^ sinbx dx =t@##tl!l*,23. !xe^ *=*r*-t)e^
+CZS. Jhx dx=xlnx-x+CRadicals
27. | --3-=sin-'I+C
'Jot -*'
cl
,n. I#=n(,+Jo\r)+c
to accompanv Stewart's CalculusIntegration Formulas
,. I+*= hlxl+ cn. []--a,=*^l#1.,6.
8.
10.
t2.t4.
16.
18.
20.
22.
Jcosxah=sinx+CJcsctr dx=-cotx+C
Jcscxcotx dx=-cscx+C
tcotx dx: hlsin-rl+ C
lcsc x dx= hlcscx - c ot xl+ C
Jcos'r 4*=!**!rin2x+C
J.or" dx =!cos'-t *rin**':J lcos'-tx dx
lar dx= o' *c) lnaJe^cos bxdx=t9##@."
24. !x'e* dx=!x'e^ *|!*''"* *26. fx' tn x dx =,
*" l.,rlc+ t) Inx- 1] + cJ (n +l)
n. !Ja' - x' ax = ;"t"' -.' +L"r,.-' ! + c
so. fft +f ax=il7.,r *ln(..k *).ct. I#=nl*+J* -,'l+cn. !J7
aax=?17 + -lnl,..t* -*l.c$. I
---3-=1r..-'
t+c, x^lx, _a, a a
34. l---L=-L^l'*Wl*,txlo'-x' a I x I
ISBN-1 3: 97 8-O-324-O1 837-0ISBN-1 O: O-324-O1 A37-1
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