Evaluate : `inte^(2x)*(-sinx+2cosx)dx`.

1.	Evaluate : `inte^(2x)*(-sinx+2cosx)dx`.
Answer» We have `I=inte^(2x){cosx-sinx}dx=2inte^(2x)cosxdx-inte^(2x)sinxdx` `=2{:[cosx(e^(2x))/(2)-int(-sinx)(e^(2x))/(2)dx]:}-inte^(2x)sinxdx` [integrating `e^(2x)` cos x by parts] `=e^(2x)cosx+inte^(2x)sinxdx-inte^(2x)sinxdx+C` `=e^(2x)cosx+C`.

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