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Chapter 5 38

# Chapter 5 38 - 470 D CHAPTERE INTEGRALS 18 Let u 2 2y4 —...

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Unformatted text preview: 470 D CHAPTERE INTEGRALS 18. Let u 2 2y4 — 1. Then du 2 8y3 dy and y3 dy 2 édu. so ﬁmf—1V”+C. 19. 20. Z1. Z3. 24. 25. 26. 27. 28. 29. 30. 31. 32. fy3v2y4—1dy =fu1/2(%dU) =€§ Let u 2 7rt. Then du 2 7rdt and dt 2 nag—LC: 1 ; du. so fsinntdt 2 fsi11u(%du)2%(—cosu)+C2 —%cos7rt+C. Letu 2 20. Then du 2 2d6 and d0 2 ldu so fsec26 tan20d02 fsecutanuﬁ du) 2 —secu+C2 2 Letu2lnx. ThendU2g 50/ (km) 37 \$ Letu 2 tan‘1 m. Then du 2 d\$ so/ 1+:c2’ dt dm2fu2d1L2lu — ésec20 +0. 3 3+C=§ (Inst)3 + C. tan’lx u (tan—11:) 1+\$2 dx—/udu—§+C————+C. Letu 2 x/i Then du— 2 — and ——dt2 — 2du so 2ff /COS\/Edt:fcosu(2du) 22\$inu+C22Sin\/E+O- ﬂ Letu 2 1 +223”. Then du 2 §\$1/2d.’17 and ﬁdm 2 gdu. so 2 fﬁsin(1+m3/2)da:2 fsinu(§ du) 2 2 3 ~(—cosu)+C2 2§COS(1+\$3/2)+C. Letu 2 sin0. Then du 2 c050d6.sofcos«9 sin69d6 2 fu6du 2 \$u7+C 2 %sin70+C. Let u 2 1 + tan 0. Then du 2 sec2 6d6, so f(1+tan9)58ec20d6 2 fu'sdu2 éuG—i-C: Letu21+em.ThendU2ewdm,sofeI\/1+e\$dac2f\/ﬁdu2§u3/2+C2 %(1+tana 6+0 0r: Letu 2 \/1 + 6”. Then 112 2 1 + eg” and 2udu 2 ex dm. so femx/1+emd:c2fu-2udu2§u3+C2 Let u 2 cost. Then du 2 — sin t dt and sin t dt 2 feCOStsintdt 2 f6” (— 2du. so 2 26” —|— C 2 —eC°St + C. Letu 21+ 23 Then du 2 322 dz and Z2 dz 2 l du, so 3 /€/‘%dZ:/“_1/S(3du): %-§u2/3+C= [oh—t (1+23 §(1 +630)”2 +C. )2/3+C. WIN (1 + em)?”2 + G. Let u 2 of + be + 0. Then du 2 2(aac + b) da: and (am + b) dw 2 édu, s0 x/ax2+2bm+c+C. _(_—am+b) dx _ d—u x/ax2+2b9:+c 2\/— LetU2lnm Thendu2 ﬂ so a; \$ln1: Letu 2 6“” + 1. Then du 2 ex doc. 30/ a: 2 22fu’1/2du2u1/2—l—C2 2/d—u2 1n1u|+C2 In!ln:c|+C. dw2 e\$+1 d_u u 2ln|ul + 02 111(61 + 1) + C. ...
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