Question

How to make a substitution and then use integration by parts to evaluate the integral.∫ e^(cost) sin2t dt ?

Answer 1

`-2[coste^(cost)-e^(cost)]+c`

Explanation:

`y=cost`
`dy=-sintdt`
`e^costsin2t=e^y(-2y)dy`
`inte^costsin2t=inte^y(-2y)dy=-2inte^yydy=-2[ye^y-e^y]+c=-2[coste^(cost)-e^(cost)]+c`