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

1 Answer
bp
Apr 23, 2015

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]#

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