Question

Find the Laplace transform of the function f (t) = 3t^4 – 2t^3 + 4e^-3t – 2sin5t + 3cos2t.

(a) 72/s^5 – 12/s^4 + 4/(s+3)+10/(s^2+25)+3s/(s^2+4)

(b) 72/s^5 – 12/s^4 + 4/(s+3)-10/(s^2+25)+3s/(s^2+4)

(c) 72/s^5 – 12/s^4 – 4/(s+3)+10/(s^2+25)+3s/(s^2+4)

(d) 72/s^5 – 12/s^4 – 4/(s+3)-10/(s^2+25)+3s/(s^2+4)

I had been asked this question during an online exam.

My doubt stems from Operational Transforms topic in portion Intoduction to the Laplace Transform of Network Theory

Answer 1

Right answer is (b) 72/s^5 – 12/s^4 + 4/(s+3)-10/(s^2+25)+3s/(s^2+4)

Best explanation: L (3t^4 -2t^3+4e^-3t – 2sin5t +3cos2t) = 3 L (t^4)-2L (t^3)+4L (e^-3t)-2L (sin5t) + 3L (cos2t) = 72/s^5) -12/s^4 +4/(s+3)-10/(s^2+25)+3s/(s^2+4).