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A9Ys d 3 d ; d :d&sd2`d+9dd%d,d%d'bd42df,dpIXd<d :d1d6Od4 dA1dh(bdf%df({d-)dXV'd3m d =Y!dh!*!d("9"d">#d\6$P%d%?&d9'+'d)(AF)d)7p*d*'N+d(u+@,d,'-d -6.d.@/dK)0It1d 1@2d3D"4df424d05B5d<6L%7dq7DP8d8H^9d9.?:dm:-:d  ;I)<dr<2=dJ=-=d>@dyAXDdE5EdE1xFFnF 0fGHHwHH4LH`H mbH<6X9`("Courier 10cpiX'dxd Level 1 Level 2 Level 3 Level 4 Level 5(2TN$ zG!XyXXXXyXXXyXXXX8yXXdd8   ($ (    ) M << deUUXXLfXXL(XXLxXX|L)XXLL XPXXL1XX[LXXLx2 )func{f(x)~=~SQRT{``1````x^2``}}XXLfXXL(XXLxXX|L)XXLLXXtLx 3 #XPXXOL1XXLXXLx/2 1func{f(x)~=~~x^3~SQRT{``1````x^2``}}XX*fXX*(XX*xXX|*)XXL*X:RXXx XYPXXL4XXLXX<Lx2 0func{f(x)~=~xOVERSQRT{``4````x^2``}}XXfXX(XXxXX|)XXLX:$XXk3XXYLx5 func{f(x)~=~3OVERx^5}XXfXX(XXxXX|)XXLX:$XX|k1XXYL3XXLx2XXLXXL1 (func{f(x)~=~1OVER{3`x^2``+``1}}XXfXX(XXxXX|)XXLX:$XXYklnXX_kxXXLx<2 !func{f(x)~=~{ln`x}OVERx^2}XXLfXXL(XXLxXX|L)XXLLXXL7XXLeB4x func{f(x)~=~7`e^{4`x}}XXLfXXL(XXLxXX|L)XXLLXXL6XXLxXXNLe(Dx,,2) "func{f(x)~=~6`x``e^{(`x^2`)}}XXLfXXL(XXLxXX|L)XXLLXXL4XXLsinXX>L3XXLx func{f(x)~=~4``sin`3x}XXLfXXL(XXLxXX|L)XXLLXXLxXXLcosXX>L2XXLx func{f(x)~=~x``cos`2x}XXLfXXL(XXLxXX|L)XXLLXXLtanXfXmXXLxd3 *func{f(x)~=~tan`LEFT(`x^3`RIGHT)}XXLfXXL(XXLxXX|L)XXLLXXtLe 2\xXXLsinXXL3XXLx "func{f(x)~=~~e^{2x}~sin`3x}XXLfXXL(XXLxXX|L)XXLLXXLarctanXXL(XXL2XX4LxXXLXX|L5XX L)XX LXX Ltan( x 1XX L(XX L2XXLxXXLXXXL5XXL) Nfunc{f(x)~=~arctan`(``2`x``+``5``)}~=~tan^{1}`(``2`x``+``5``)XXLfXXL(XXLxXX|L)XXLLXXLarctanX"fX"mmXZOXXLx 2func{f(x)~=~arctan`LEFT(``SQRTx``RIGHT)}XXLX$XXk1XX%L(XXL3XXWLxXXLXXL2XXCL)2XXdx 0func{INT~1OVER{(``3`x``+``2``)}^2~dx}XX`L" XXXK1XX%L2XXLxXXWLXXL1XXdx 'func{INT~1OVER{2`x``+``1}~dx}XXLXXx XXXPXXx2XXXX4XXdx ,func{INT~x``SQRT{x^2``+``4``}~dx}XXLm X$XXk4XX%Lx2XX9LXXL1XXdx *func{INT~4OVER{x^2``+``1``}~dx}XXL X$XXkxXX%Lx2XX9LXXL1XXdx 'func{INT~xOVER{x^2``+``1}~dx}XXLXX4XXsinXX 3XXxXXRdx func{INT~4``sin`3x~dx}XXLXX7XXve4^xXXdx func{INT~7`e^{4x}~dx}XXLXXxXXe$4txXXdx func{INT~x``e^{4x}~dx}XXLXXxXXe$(x,,21)XXdx #func{INT~x``e^{(`x^2`)}~dx}XXLXXxXXcosXX xXXdx func{INT~x``cos`x~dx}XXLX$XXHk1XX%Lx2XX9LXXL2XXkLxXXZdx )func{INT~1OVER{x^2``+``2`x}~dx}XXLX$XXkxXXHkXXk5XX%Lx2XX9LXXL2XXkLxXXZdx 3func{INT~{x``+``5}OVER{x^2``+``2`x}~dx}XX`LXXX%KlnXX+KxXXLxXXdx func{INT~{ln`x}OVERx~dx}XX`L3XXXKcosXXGKxXX%L1XXLXXmLsinXXLxXXdx /func{INT~{cos`x}OVER{1``+``sin`x}~dx}XX*fvXX*(XXP*xXX*)XX*XRXXXX x XPXX@L1XXLXXLx 2 4func{f'(x)~=~{x}OVERSQRT{``1````x^2``}}XX*fvXX*(XXP*xXX*)XX*eXRXXXXu4XXx4XXXX3XXIx2  XPXX6L1XXLXX~Lx2 Ffunc{f'(x)~=~~{4`x^4``+``3`x^2}OVERSQRT{``1````x^2``}}XXfHXX(XXPxXX)XX~X$XXk4XXL(XXIL4XXLXXLx)2XXL)3m/2 5func{f'(x)~=~4OVER{(``4````x^2``)^{3/2}}}XXfHXX(XXPxXX)XXFX$XXkXXk15XXLx}6 !func{f'(x)~=~{15}OVERx^6}XXfHXX(XXPxXX)XXX$XXkXXk6XX kxXXL(XXIL3XXLxo2XXLXXL1XX3L)2 7func{f'(x)~=~{6x}OVER{(``3`x^2``+``1``)^2}}XXfHXX(XXPxXX)XX!X$XXk1XXIkXXk2XXklnXXkxXXLx~3 -func{f'(x)~=~{1````2``ln`x}OVERx^3}XXLfXXL(XXPLxXXL)XXLXXhL28XXnLe4dx func{f'(x)~=~28`e^{4`x}}XXLfXXL(XXPLxXXL)XXLXXhL(XX L12XXLx2XX&LXXL6XXnL)XXLe( x,,m 2 ) 6func{f'(x)~=~(``12`x^2``+``6``)``e^{(`x^2`)}}XXLfXXL(XXPLxXXL)XXLXXhL12XXLcosXXL3XXzLx func{f'(x)~=~12``cos`3x}XXLfXXL(XXPLxXXL)XXLXXhLXXL2XXnLxXXLsinXXL2XXLxXXLXXPLcosXX L2XXF Lx ,func{f'(x)~=~2`x``sin`2x``+``cos`2x}XXLfXXL(XXPLxXXL)XXLXXhL3XXLx2XX Lsecr2XfXmXX Lx3 6func{f'(x)~=~3`x^2``sec^2`LEFT(`x^3`RIGHT)}XXLfXXL(XXPLxXXL)XXLXXLeX2xXX$L(XXL3XXlLcosXXL3XXbLxXX LXX L2XXN LsinXX L3XXD LxXX L) ?func{f'(x)~=~~e^{2x}``(``3``cos`3x``+``2``sin`3x``)}XXfHXX(XXPxXX)XX}X$XX+k1XXL2XX3Lx2XXGLXXL10XXLxXXLXX9L13 6func{f'(x)~=~1OVER{2`x^2``+``10`x``+``13}}XX fVXX (XXP xXX )XX fX2XXy1XXL2XX3L(XXLxXX{LXXL1XXL)XQOXXLx :func{f'(x)~=~1OVER{2`(``x``+``1``)`SQRTx}}" X2XXKXXxK1XXQL9XXLxXXLXX'L6XXXXc (func{{1}OVER{9`x``+``6}~+~c}]X(B1B82XXlnXX XXZ2XXxXXXX01XX XX|XXLc 8func{1OVERSM2``ln`LINE``2`x``+``1``LINE~+~c}]X(B1B83XdfXdmXX0x2XXDXX43/g2XXXXc Bfunc{1OVERSM3``LEFT(``x^2``+``4``RIGHT)^{3/2}~+~c}XXL4XXLarctanXXLxXXnLXX>LcXXLXXL4XXLtan: 1XX LxXX LXXV Lc :func{4``arctan`x~+~c~=~4``tan^{1}``x~+~c}]X(B1B82XXlnXdfXdmXX6x2XXJXX1XX%XXc >func{1OVERSM2``ln`LEFT(``x^2``+``1``RIGHT)~+~c}XX]X483XXPcosXX3XXFxXXXXc $func{4OVERSM3``cos`3x~+~c}]X(B7B84XXep4xXXhXX8c #func{7OVERSM4``e^{4x}~+~c}]X(B1B84XXxXXPe48xXX Xl1816XXVe4>xXXXXc ?func{1OVERSM4`x`e^{4x}````1OVERSM16`e^{4x}~+~c}]X(B1B82XXep(x,,32})XX%XXc (func{1OVERSM2``e^{(`x^2`)}~+~c}XXLxXXLsinXX6LxXXLXXLcosXXTLxXX$LXXLc #func{x``sin`x~+~cos`x~+~c}XX`L5XXX%K1XX%L2XXJhXX jXXjXXiXXoJoXXo qXXoqXXop5XXXK1XXLxXX" XEXXKXXDK1XXdLxXXLXXL2XXEdxXX5X{ XX K1XX L2XD] eXDlXX lnXX  XX! xXX  XX+ XX lnXX XXQxXXXX2XX= XXLXXc func{INT~1OVER2``LEFT(``1OVERx``+``{1}OVER{x``+``2}``RIGHT)~dx~=~1OVER2``LEFT(``ln`LINE`x`LINE````ln`LINE``x``+``2``LINE``RIGHT)~+~c}XX`LXXJhXX jXXjXXiXXJoXX qXXqXXpFXXXK5XX8K/XXK2XX8LxXXs X5XXTKXXK3XXDK/XXK2XXdLxXXLXXL2XXUdxXX5X XX K5XX L2XXm lnXXs  XX xXXg  XX 5X XX K3XX L2XXlnXX XX xXXXXQ2XX XXXXmc func{INT~LEFT(``{5/2}OVERx``+``{3/2}OVER{x``+``2}``RIGHT)~dx~=~5OVER2``ln`LINE`x`LINE````3OVER2``ln`LINE``x``+``2``LINE~+~c}]X(B1B82XX(XX|lnXXxXX&)2XXFXXc +func{1OVERSM2``(``ln`x``)^2~+~c}XXLlnXXL(XXL1XXbLXXLsinXXLxXX(L)XXLXXLc 'func{ln`(``1``+``sin`x``)~+~c}3|x<6X9`("Courier 10cpiXx6X@8;X@(G$XyXXXXyXXXyXXXX8yXXdd8  @8P!erdU zG!XyXXXXyXXXyXXXX8yXXdd8   ݛREVIEWPROBLEMSONDIFFERENTIATIONANDINTEGRATION  PART(A):Inthisset,findandsimplifythederivativeofthefunction.  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(14)#"VFBz X ~ 0 @Xdddddddd@E(#dd@#M   #   ^&j" PART(B):Inthisset,findtheindefiniteintegral(antiderivative)asindicated.CHECKanswersbytakingtheirderivatives.Inmost,youmustusesubstitution.Insome,youmustuseintegrationbypartsorbypartialfractions.(1)%$VFBz X ^ 0 @Xdddddddd@E OddL\    (2)'&VFBz X  0 @Xdddddddd@E ddL3    (3))(VFBz X r 0 @Xdddddddd@EN|KddLD NZ  (4)+*VFBz X  0 @Xdddddddd@EddL4   (5)-,VFBz X  0 @Xdddddddd@EoddL a o{  (6)/.VFBz X  0 @Xdddddddd@EF%ddW]L FR  (7)10VFBz X  0 @Xdddddddd@Ej%dd ]L jv  (8)32VFBz X  0 @Xdddddddd@E%dd!]L*  (9)54VFBz X  0 @Xdddddddd@E?ddwLNn  (10)76VFBz X  0 @Xdddddddd@E(%dd]o  (11)98VFBz X / 0 @Xdddddddd@E("'dd_! "  (12);:VFBz X / 0 @Xdddddddd@E($'dd_$ $  (13)=<VFBz X  0 @Xdddddddd@E('dd^' '# (14)?>VFBz X  0 @Xdddddddd@E(y*dd*o y*&   0-<) PART(A):answers,simplified(1)A@VFBz X  0 @Xdddddddd@Epdd>L ` p| (2)CBVFBz X & 0 @Xdddddddd@Eu - &dde^L  u  (3)EDVFBz X  0 @Xdddddddd@E ddAL6    (4)GFVFBz X  0 @Xdddddddd@Eq ddAL  q}  (5)IHVFBz X  0 @Xdddddddd@EHdd/L   HT (6)KJVFBz X  0 @Xdddddddd@E ddCL! + (7)MLVFBz X  0 @Xdddddddd@EddLY"   (8)ONVFBz X  0 @Xdddddddd@E dd 3Lj #   (9)QPVFBz X  0 @Xdddddddd@EddLd$   (10)SRVFBz X  0 @Xdddddddd@E( dd <c %   (11)UTVFBz X  0 @Xdddddddd@E(x ddH & x  (12)WVVFBz X + 0 @Xdddddddd@E(P!=ddu  ' P!\ (13)YXVFBz X % 0 @Xdddddddd@E((#% dd] " ( (#4 (14)[ZVFBz X ; 0 @Xdddddddd@E(%4 ddl% ) % "   )% PART(B):answers,simplified(1)]\VFBz X I 0 @Xdddddddd@ED;ddsL* DP (2)_^VFBz X  0 @Xdddddddd@E 8ddpL i+   (3)a`VFBz X 8 0 @Xdddddddd@E2 48ddlpL , 2 > (4)cbVFBz X  0 @Xdddddddd@Ei dd Ls - iu  (5)edVFBz X N 0 @Xdddddddd@EAJ8ddpL. AM  (6)gfVFBz X I 0 @Xdddddddd@Ex;8ddspL/ x  (7)ihVFBz X  0 @Xdddddddd@E8ddpLKU0   (8)kjVFBz X  0 @Xdddddddd@E 8ddCpL1߀[integrationbyparts]   (9)mlVFBz X L 0 @Xdddddddd@EJKddL2 )  (10)onVFBz X E 0 @Xdddddddd@E(gIdd 3߀[integrationbyparts] gs  (11)qpVFBz X 9 0 @Xdddddddd@E(qdd-94߀[partialfractions] + (12)srVFBz X  0 @Xdddddddd@E( dd-5߀[partialfractions]   (13)utVFBz X y 0 @Xdddddddd@E(#k8ddp"36 # (14)wvVFBz X  0 @Xdddddddd@E(>%ddU$7 >%J! М