I can get you started on the second one . . .
∫ x▓(1 + x▓)^Ż dx, .using the substitution: x = tanθ
We have: .x = tanθ . → . dx = sec▓θĚdθ
. . and the radical becomes: secθ
Substitute: .∫ tan▓θĚsecθĚsec▓θĚdθ . = . ∫ sec│θĚtan▓θĚdθ
This integral is particularly annoying to integrate.
. . It has an odd-powered secant and an even-powered tangent.
It requires integration by parts and some fancy algebra.
I'll jump to the punchline:
. . (1/8)[2Ěsec│θĚtanθ + 3ĚsecθĚtanθ + 3Ěln|secθ + tanθ|] + C
and let you back-substitute . . .