\int t.e^{-t}.dt\text {, Since this is a product of two different functions, you need to use integration by parts }\\\text{let: } u=t,u'=1\text{ ,you let u =t as it's simpler to integrate the exponential}\\v=-e^{-t},v'=e^{-t}\\\text{ integration by parts: } uv-\int vu'.dt\\\therefore \int...