Question

Please the Mathematica and show the syntax please

1.) Evaluate the following integrals: X 2 1a.) S dx x(3x+1) 1b.)S dx x-

Answer 1

la) Given 2 du 2 (34+) 2 J = (2x+ de (34+) By partial de composition of A B = f n (3xH) 3241 1-A(BxH) + B x a(3uH) x(304) 1- A (32H) +Bu Put x=0 1= A ( 30) +) +Blo IA

put x = -1/3 174(3(-)1) + (-) [ = A (+1) -R 1-0- ९ AM ६ = 8- *:Se descnxe] --3 श du 4 (341) - 2 du K. * +51) = [ Jax - २ २ 3 3xi - 2 (.np- 6 (n (32+HD rt 3

- 2 Inbul- & (n(134+1) +C elinler - In 15x+11)) + c Ver mais dx = 241 mpe) – in (3x+10) 221344) ta 16) (given e dre Jet substitute See = fu x-1 = U -) X=U+1 dx=do x da - Jut U1 ro du 1-1 se to do لال = sold do - SJU du + As to do undo wkt . ин x ht

해 +( T에 = 4 4C Jt 에서 애와 + 5 min + ㄴ =2 to 4C 3 , Undo substitution 서 2 (1) +2서 서 3 서 세 to say to 3 M (세 61 tc 3 =9월(143 +C 3 dn 서 (X+2 서 + C 3