Question

20 POINTS ! Evaluate ∫ e3x cosh 2x dx

A. 1/10e5x + 1/2ex + C B. 1/4e3x + 1/2 x + C C. 1/10e5x + 1/5 x + C D. 1/2e5x + 1/2ex + C

Answer 1

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

Solution:
substitute the identity

`cosh(2x)=(e^(2x)+e^(-2x))/(2)`
into integral

`I=\int{e^(3x)cosh(2x)dx}`

`=\int{e^(3x)(e^(2x)+e^(-2x))/(2)dx}`

`=\int(e^(3x+2x))/(2)+(e^(3x-2x))/(2)dx`

`=\int(e^(5x))/(2)+(e^(x))/(2)dx`

`=(e^(5x))/(2*5)+(e^(x))/(2)+C`

`=(e^(5x))/(10)+(e^(x))/(2)+C`