Integral Hints
Use substitution with w = x2, then integration by parts, then finish up by taking the limit.
Use substitution with w = 1 + z2, get an integrand of (w-1)2 /(2sqrt(w)).
Either use integration by parts twice with boomerang, OR, rewrite 23x as e(3\ln(2))x, then use the table.
Either use substitution with w = x-1 OR use tabular integration with u = x3; Be careful with the dv!
Start with substitution: w = sin(x); after that, factor the bottom and use partial fractions.
Use substitution: w = x2 (so that the bottom becomes w2+1.)
Make the substitution w = x-1, then break into three fractions (not partial fractions, though!)
Multiply the top and bottom by ex, then substitute w = ex.
Substitute w = x2+1; you'll then have to use integration by parts, with u = arcsin(w).
Compare this integral to the one whose integrand is e-2x, which we know converges (and can show it, too ;))
Rewrite the ln term as (1/3)ln(3x+1), then use integration by parts.