Evaluate $$\! \int t^2e^{-t^3} \ \mathrm{d}t$$ using integration by parts.
I know how to use substitution to evaluate this integral, when I use integration by parts letting $u = e^{-t^3}, \mathrm{d}v = t^2\ \mathrm{d}t$ I get $$\frac13t^3e^{-t^3}+\int\! t^5e^{-t^3}\ \mathrm{d}t$$ but this leads me to nowhere. Thanks