Question

20 POINTS ! Evaluate ∫ e3x cosh 2x dx

Answer 1

Question:
Evaluate $\int{e^{3x}cosh(2x)dx$

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