Question

how to integral t sinh mt dt

Answer 1

\[\int\limits(t \cdot \sinh(mt) \cdot dt\]

Answer 2

Integration by Parts??

Answer 3

You can try : \[ \int t\sinh(mt)dt=\int t\left( \frac{e^{mt}-e^{-mt}}{2}\right)dt=\frac{1}{2}\left[\int te^{mt}dt-\int te^{-mt}dt\right]\] and try integrating by parts on each integral.