Question
evaluate the integral of
(e^3x)(cosh)(2x)(dx)
A.(1/2)(e^5x)+(1/2)(e^x)+C
B.(1/10)(e^5x)+(1/2)(e^x)+C
C.(1/4)(e^3x)+(1/2)(x)+C
D.(1/10)(e^5x)+(1/5)(x)+C
(e^3x)(cosh)(2x)(dx)
A.(1/2)(e^5x)+(1/2)(e^x)+C
B.(1/10)(e^5x)+(1/2)(e^x)+C
C.(1/4)(e^3x)+(1/2)(x)+C
D.(1/10)(e^5x)+(1/5)(x)+C
Answers
I did your last one by parts. Try the same trick again.
http://www.wolframalpha.com/widgets/gallery/view.jsp?id=a86aa57ade541fdb14f856fabd997a5e&sms_ss=googlebuzz&at_xt=4d11ee86a3a10396%252C0
Use for function
e^(3x)*cosh(2x)
use for variable
x
e^(3x)*cosh(2x)
use for variable
x
(e^3x)(cosh)(2x)(dx)
but cosh 2x = (1/2) (e^2x + e^-2x)
so
(1/2) [ e^5x + e^x ] dx
(1/10)e^5x + (1/2)e^x + c
so B
which we already knew from Wolfram
but cosh 2x = (1/2) (e^2x + e^-2x)
so
(1/2) [ e^5x + e^x ] dx
(1/10)e^5x + (1/2)e^x + c
so B
which we already knew from Wolfram
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