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

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Mathematics

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24 June, 14:13

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

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Cecilia Huber · 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