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Integrate the following functions e^(2x)...

Integrate the following functions `e^(2x) sinx`

Text Solution

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Let I = `int e^(2x) sinx dx,` Then
I = `e^(2x)(-cosx)- int e^(2x) xx 2 xx -cosx dx`
=`-e^(2x) cosx+2 int e^(2x) cosx dx`
=`-e^(2x) cosx+2[e^(2x) sinx- int e^(2x) 2 sinx dx]`
=`-e^(2x) cosx+2 e^(2x) sinx - 4I`
`gt 5I = -e^(2x) cosx+2 e^(2x) sinx`
= `e^(2x)[2sinx-cosx]`
`gt I = e^(2x)/5[2 sinx-cosx]+c`
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