Démontrer les formules suivantes

J2 + C0S.Ï y3 VV3 2^

Ji — 2rcosx-\-r^ 2 *Vi— ^ 2/

j ;V* COS X dx = sin x {x^ — 12 ;v2 + 24) + cos ;tr (4 ;ir3 — 24,^) + C.

1 e"^ COS- v ^■v:= ^^„ , ,^ (fl- cos- X + 2a sin .v cos .r -f 2) + C.

a (fl- + 4) a {a^ + 4)

e"^ sin- .r ^-v= — r- {a^ sin- .r — 2a sin ;v cos .r + 2) + C.

P Log X dx = ^( Log X - ^) + C.

({].ogx)"dx = x[Logx)"—n{Logx)"-^ + n{n — i){Logxy'-^ — -]-\-C.

("(arc sin .v)- rf.v = x [(arc sin a;)- — 2] + 2 (arc sin x) \Ji — x^-{- C.