Laplace tranform of $t^{5/2}$ It is asked to transform $t^{5/2}$.
I did $t^{5/2}=t^3\cdot t^{-1/2}$. Then followed the table result $$L\{{t^nf(t)}\}=(-1)^n\cdot\frac{d^n}{ds^n}F(s)$$
However i got $\frac{1}{2} \cdot\sqrt\pi \cdot s^{-7/2}$ instead of $\frac{15}{8} \cdot\sqrt\pi \cdot s^{-7/2}$.
Can you help me with the derivations?
Thanks

Using the result  $$L\{{t^nf(t)}\}=(-1)^n \cdot\frac{d^n}{ds^n}F(s).$$


*

*$t^{5/2}=t^3\cdot t^{-1/2}$.

*$ L(t^{-1/2})=\sqrt{\large\frac{\pi}{s}}=s^{-1/2}\sqrt{\pi}$, now apply the result.

$$L\{{t^3\cdot t^{-1/2}}\}=(-1)^3\cdot\frac{d^3}{ds^3}\{s^{-1/2}\sqrt{\pi}\}=\frac{15}{8}\sqrt{\pi}\cdot s^{-\frac{7}{2}}.$$

