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. |