What is the integral of $e^(5x) *cos 3x dx$ ?

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Answer 1 · 2015-04-23T03:56:16

This can be solved by successive application of the product rule of integration

$int e^(5x) cosx dx$ = $e^(5x) sinx - int 5e^(5x) sinx dx$

= $e^(5x) sinx - 5[-e^(5x)cosx - int -5e^(5x)cosx dx]$

= $e^(5x)sinx$ + $5e^(5x)cosx$ -25 $int e^(5x)cosxdx$

26 $int e^(5x) cosx dx$ = $e^(5x)sinx$ + $5e^(5x)cosx$

$int e^(5x) cosx dx=1/26[ e^(5x)sinx +5e^(5x) cosx]$

What is the integral of e^(5x) *cos 3x dxe^(5x) *cos 3x dx?