`int_0^t e^s sin(t-s) ds` Evaluate the integral

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You need to use integration by parts, such that:

`int udv = uv - int vdu`

`u = e^s => du = e^s ds`

`dv = sin(t-s) => v = (-cos(t-s))/(-1)`

`int e^s sin (t-s) ds = e^s*cos(t-s) - int e^s*cos(t-s)ds`

You need to use parts again, for `int e^s*cos(t-s)ds` , such that:

`u = e^s => du = e^s ds`

`dv = cos(t-s) => v = (sin(t-s))/(-1)`

`int e^s*cos(t-s)ds = -e^s*sin...

(The entire section contains 248 words.)

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