Question:
Evaluate [tex]\int{e^{3x}cosh(2x)dx[/tex]
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]
