Evaluate the following integrals:
`inte^(2x)sinxdx`

Explanation

Integrating by parts, we get
`inte^(2x)sinxdx=(e^(2x)*intsinxdx)-int{(d)/(dx)(e^(2x))*intsinxdx}dx`
`=e^(2x)*cosx+2inte^(2x)cosxdx`
`=-e^(2x)cosx+2[(e^(2x)*intcosxdx)-int{(d)/(dx)(e^(2x))*intcosxdx}dx]`
[integrating `e^(2x)` cos x by parts]
`=-e^(2x)cosx+2e^(2x)sinx-4inte^(2x)sinxdx+C`.
`:.5inte^(2x)sinxdx=e^(2x)(2sinx-cosx)+C`
`or" "inte^(2x)sinxdx-(1)/(5)e^(2x)(2sinx-cosx)+C`.