ecall the integration by parts formuala:\

\\\\int f(x)g^(')(x)dx=f(x)g(x)-\\\\int f^(')(x)g(x)dx

\ omplete the following computation

\\\\int e^(2x)cos(2x)dx

via integration by parts. Set\

f(x)=e^(2x) and g^(')(x)=cos(2x)

\ Find

f^(')(x)

and

g(x)

where

g(x)

has no constant term:\

f^(')(x)=\ g(x)=

\ Using the integration by parts formula,\

\\\\int e^(2x)cos(2x)dx=F(x)-\\\\int G(x)dx\ F(x)=\ G(x)=

\ Using integration by parts to compute

\\\\int G(x)dx

, find

H(x)

and a constant

c

such that\

\\\\int e^(2x)cos(2x)dx=,F(x)-(H(x)-c\\\\int e^(2x)cos(2x)dx)\ H(x)=,c=

\ Use (1), (2), (3) to compute

\\\\int e^(2x)cos(2x)dx=

ecall the integration by parts formuala: f(x)g(x)dx=f(x)g(x)f(x)g(x)dx omplete the following computation e2xcos(2x)dx via integration by parts. Set f(x)=e2xandg(x)=cos(2x) 1. Find f(x) and g(x) where g(x) has no constant term: f(x)=g(x)= 2. Using the integration by parts formula, e2xcos(2x)dx=F(x)G(x)dx G(x)= 3. Using integration by parts to compute G(x)dx, find H(x) and a constant c such that e2xcos(2x)dx=F(x)(H(x)ce2xcos(2x)dx)H(x)=21e2xcos(2x) c= 4. Use (1), (2), (3) to compute e2xcos(2x)dx=