Question

evaluate the integral

(c) C os(3x)dx

Answer 1

let that such then Let Integration by parts f(x) & gran be two integrable functions f'la is also integrable Strange a dx = f(x) { goal dx - ( f(x) ( ger dx) de f(x) = e PR - gox) = cos(3x) Then Seze cos (38) does és cosex) dx.- Sae2x ( scos (3x) dx) dx e 22 sin(x) - 2 je 2 sinBx) dx 464)32222 [:'s cos cax) dx = Sincaz) -) Se 2* cos(32d2= 1/3 e 22 sin (3x) - 2/3 sexsin (3x) dx.tc, [c, is the constant of integration] Now, using integration by parts again, we se za 2x sin (3x) dx = (2x / sin (3x) dx - sa e 2x (ssin6x) dx) dx €2% (-COS (x)) :(sinland de = 3 3 have ene cos6") - 2 Se266-c03c8x) dx [governo 3 =) Se 22 Sin (3x) dx = -1 e 2x cos(3x) + 25 Sex 3 cos (3x) dx tc2, [c₂ is the constant of integration

Seby O, Ser cos (3x) dx = e sint 3 ) - [Jer cos (3x)+ Setos (x) dz + cs] 커디 -) [ex CCs 3)dx = v exsin(33) + 음 ex cost ex) - = Setog(3) dx 를 C2 키 Se2 cos(37)dx tg Seosc37)de =놓ea [Sn(3)t클cos(320] +s [Taring 3대를에 목 Se29c0s(32) dx = 쪽 [Sinc3x) +를 cos (32] t3 =) sex cos(3x) dx = 잃 [Sinc3x)t를 Cost3] 1월 3 . De [sin(x) + 을 Cos (sx)] + c [rating 년 옵 e2 Seicos(3x)dx = [ 3 sis (3x) + 2 COS (3x)] + c 3 Q. 13 3 13 13