Solution: substitute the identity [tex]cosh(2x)=\frac{e^{2x}+e^{-2x}}{2}[/tex] into integral [tex]I=\int{e^{3x}cosh(2x)dx}[/tex] [tex]=\int{e^{3x}\frac{e^{2x}+e^{-2x}}{2}dx}[/tex] [tex]=\int\frac{e^{3x+2x}}{2}+\frac{e^{3x-2x}}{2}dx[/tex] [tex]=\int\frac{e^{5x}}{2}+\frac{e^{x}}{2}dx[/tex] [tex]=\frac{e^{5x}}{2*5}+\frac{e^{x}}{2}+C[/tex] [tex]=\frac{e^{5x}}{10}+\frac{e^{x}}{2}+C[/tex]
