Use Laplace transform (with respect tot)to calculate the integral

I=\int([\cos(tx)/(x^2+a^2)]dx t\geqslant 0

[IMG]file:///C:/Users/Jamie/AppData/Local/Temp/msohtmlclip1/01/clip_image002.jpg[/IMG]

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- May 11th 2011, 06:45 AMsublim25Laplace transform to calculate an integral.
Use Laplace transform (with respect to

*t**)*to calculate the integral

I=\int([\cos(tx)/(x^2+a^2)]dx t\geqslant 0

[IMG]file:///C:/Users/Jamie/AppData/Local/Temp/msohtmlclip1/01/clip_image002.jpg[/IMG] - May 11th 2011, 06:54 AMTheEmptySet
- May 11th 2011, 07:02 AMsublim25
Limits are from 0 to infinity.

- May 11th 2011, 07:41 AMTheEmptySet
Let

Then

Now by partial factions we get

Now if you take the inverse Laplace transform we get

- May 11th 2011, 07:45 AMsublim25
Can you please explain how you get the partial fractions to come out to this?

- May 11th 2011, 07:54 AMTheEmptySet
- May 11th 2011, 08:24 AMsublim25
I am not sure what I am doing wrong, but when I solve the system, everything is cancelling out.

- May 11th 2011, 08:38 AMTheEmptySet