Question

Evaluate ∫ e3x cosh 2x dx A.1/ e5x+1/ex+C 10 2 B. 1/ e3x + 1/ x + C 42 C. 1/ e5x + 1/ 10 5 x + C D. 1/ e5x + 1/ ex + C 22

Answer 1

sh(2x) = (e^2x + e^-2x)/2

Thus the integral becomes

Int[e^3x*(e^2x + e^-2x)/2] = Int[(e^5x + e^x)/2]

= e^5x/10 + e^x/2 + C
=(1/10)(e^5x) + (1/2)(e^x) + C