I am in the middle of solving a integro-differential, and I need to use inverse Laplace transforms to complete the last bit, I have the following:
![<br />
x(s)= \frac{1}{s\left[1+\frac{s}{s+1}\right]}+ \frac{1}{s^2\left[1+\frac{s}{s+1}\right]}-\frac{1}{s+1\left[1+\frac{s}{s+1}\right]}<br />](http://latex.codecogs.com/png.latex? <br />
x(s)= \frac{1}{s\left[1+\frac{s}{s+1}\right]}+ \frac{1}{s^2\left[1+\frac{s}{s+1}\right]}-\frac{1}{s+1\left[1+\frac{s}{s+1}\right]}<br />
)
I have simplified this to the following form:
= \frac{s+1}{s(s-2)}+\frac{s+1}{s^2(2s+1)}-\frac{s+1}{(s+1)^2+s}<br />
)
Then using partial fractions I have taken the above term by term, and done the following:
} = \frac{-1/2}{s}+\frac{3/2}{s-2}<br />
)
Second term:
} = \frac{-1}{s}+\frac{1}{s^2}+\frac{2}{2s+1}<br />
)
Can some please varify if I have used partial fractions correctly on the first 2 expressions
Also I do not understand how to use partial fraction on the third expression, can some please help and explain how I would do this... ?
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Originally Posted by ubhik
I am in the middle of solving a integro-differential, and I need to use inverse Laplace transforms to complete the last bit, I have the following:
