Laplace Transform of $e^t\cos(3t)\operatorname{heaviside}(t)$

Question

Find the Laplace Transform of $e^t \cos(3t) \operatorname{heaviside}(t)$

Since $\operatorname{heaviside}(t)g(t) = \mathcal{L}(g(t)) $ and $\mathcal{L}(e^t\cos(3t)) = \frac{(s-1)}{(s-1)^2+9} $ the solution should be$\ \frac{(s-1)}{(s-1)^2+9} $ but Wolfram Alpha Laplace calculator says it is $\frac{(s-1)}{(s-2) s+10}$

What am I doing wrong?

Answer 1

Your work agrees exactly with Wolfram Alpha's. Try expanding the denominator of your expression and the denominator of Wolfram Alpha's expression.