Question

Please help me and show all the steps and please make sure it's correct 4&6

[ 7 pts.] 4. Use an appropriate trig substitution to integrate x dx | ? -67 +5

Answer 1

J a da hall " 62-64+5 = dx ल-33 Apply U–Subslotutoon U=x-3 =1 du de=du & du M J J ſuz-a [ u=x-3 2 ut3 de x=ut3 Vuz_4 Espad, 3 Just + 4) du 3 Apply the sun rule Je du dut = Vu²4 first, Just du un substitution v=u2-4 Apply du du - 2u & dua 1. du 20 = vo z dv = Java do - 2 Juk av ŹCE (with vatl - 1/2+1

Y2 = va find, J Jerry du du = 3 .31 1 ² (Juz 4 tu) | Ź .2 cvjle substitute back u²_4 Take the constant out 3 J Just ad Apply thy substitution u = 2seCCU) 2 seccus. fancy) du=aseccos. tancu).dv 2 seeru). tancus.du simplify 3) secu). du = 3 Ini tan()+ secas substitute back (tau) =3h/tan Carc sec(sust sec Carc sec (32")) simplify du dv =3 Sresecu)3=4 are see =

from @ = vuz_4 + 30 l Ž Cruz 4 + U) substitute back u=X-3 13-333–4 +31 1 g2-332-4+(-3)) | simplify 7²_6+5 + 30 l Ž (J22-68+5 +X-31 Add constant to the souton a VaRx+5 + 3h | Ž CJX2_64+5 +X-31 tc Thank you