Question

(a) [(5.12 (5x2 + 1)e3x dx

Answer 1

Given that S (52+1) est de • sfx* det je da =5[*?..? - Se 4 (22) de] en ( Integeatics by parte, ste - fee fx ex de s[sze3 Jest ride of 32 e 3 2 32 e 3 = 3 de) Jelena Jeprodu] 3x 2 32 xe .x²e 3X de I fe f 9 scenen 32 ex fc f 2.32 x e3x *е37 — 10 хе {xe32 3xf 10 10 xe 9 3 3 9 32 32 10 e3x fe xe ifc 3 2 32 e32fc 10 x e3x + 19 - To ca rx et 27 3 G Given that s Cos (J7) de put a=t I dx = dt ara e) de = ada di > dx = 2t at

- 2 Cost It Sal (Ve) dx = f cost atat 2S+ 2 [t. (Sant)- Jent).1 dt] [t sint + Cost] + c [ve Cos de] fc 2 sindă f 2 Given / corso Cosso do Coso do s Core² sesino) ² caso do put smot Coro do=dt = f Q-tedt = f (1778-2+²) at Sdt t . t t at -2 ft²dt = tf zľfc fc 3 sino f simso 2 sinofc - 5 3

Б s (see see 32 + Col 384 dse see3x f CB3% f 28203x 083x)dx = s see 3x dx f/ Coel 3x dx + 2 ft Case de 6862) dx + 2 12 Jdx lan 32 t det į / 686x de + 2x flos 6x tan 32 t S(144 3 = 3 Sinox) + 2x + c tan 32 f { x + Ź 6 3 tan 3x X f Sinox f 2x fc - f 12 2 3 ben 3x 1 Sin 6x + 5x + c - f 12 3