∫tlntdt
=1/2∫lntd(t²)
=1/2[t²lnt-∫t²d(lnt)]
=1/2[t²lnt-∫tdt]
=1/2t²lnt-1/4t²+C
∫te^tdt
=∫td(e^t)
=te^t-∫e^tdt
=te^t-e^t+C