Question

evaluate the integrals

Evaluate the inte integrals: a. Stsec at at 72 C: X.COS. T dx dx. b. Luxe 2x (1+2x)? d. frinrar

Answer 1

Evaluate the integrals. a) s t sec“ 2 t) dt we have to sole this integral through by pauts & using TLATE usude - Scuisudx) de uuda °C > CD) Sit seezt dt t (sec²(2t) at - SC1. ssec cet) ott) at (I) (U) tanzt dt. t. tanzt 2 (sec°(et) po 1 2 2 dt. t.tanat 2 Sinzt Cosat . [ A recen tank to Sseendu = t tannt + dt 2 Sin COS25 2 4 11 ttanzt + 1 2 da log| cos2t].+c (Ares) [as. Se log belte +] Ź (2e**, dix (+22)? (multiplying by 2 CNidors) da. (+2x)* 24 1. 2 da ((1+22-1) e? (1+2x)

an du (1+228" I c Ii let I 1 It seems that the © & Lende Servering dx. (Hrn) using By pauts and ILATE Sunda ufvere - Slijven) on (142x) tt ſe de us* fe2dx) dx Sluttres 1 Seite 2 e2n de I = 1 CO) (I) Vlaky (2 423 2 (H2x) 2x 2x da X2 I 2 I I 2 (tau) 2 2 ex I. = da of į 4 CH2x) Il Pulting the value of in equation © + 1 real de 2x I e Senten de (H2a)2 2 4C1+2x) T eza tc 40 +2x) (Ars)

/2 (C) S x Cos I due COST from some [*1. nt 24 COST (6)?-(034] ( 41.fpende nti 2 C Cusli X 1 2 costi=-1 - 1 8 II C: -3] Ary c) using ILATE. 3 3 I wenner Suvdx usudoe- saljudu) du. I : Si Alnader [ logo (osor] - 1 h Srbar) dr - florer ") ar 1 Serior. = *( 3+ log 3 - logicion] - [A"), 3 e 3

81 log 3 U -0 [nl-no] 4 4 ܙ ܐ 81 क log: 3 80 16 81 4 log 3 - 5 : -5 + 81 log 3 4 (Ans)