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Evaluate : inte^(2x)*(-sinx+2cosx)dx. |
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Answer» Solution :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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