Determine L^-1{F}. s^2F(s) - 4sF(s)

Transcript

00:01 So we have given here the integration 3x square whole upon x square plus 7 to the power 3 by 2.

00:20 Now to solve this integration let's put first here put x is equal to under root 7 10 u and now we need to differentiate this so dx is equal to then we have under root 7 sec square u.

00:43 So after putting here the value of this given term we will get integration and we have here then take 3 outside so it become from here under root 7 square 10 square u which is value of d and we need to integrate this with respect to dx and this is the value of x multiply with value of dx that is under root 7 sec square u and whole upon we need to write here that is 7 10 square u plus 7 to the whole power 3 by 2.

01:32 So after simplify this we will get from here that is in 3 integration we need to write here then 7 to the power 3 by 2 10 square u into sec square u and whole upon we need to write here 7 to the power 3 by 2 take 7 outside and it becomes from here that is sec u so after simply because 1 plus 10 square is sec square.

02:12 So after simplify this we will get from here that is integration of this 2 term will be cancel and this square cancel by cube so it becomes 10 square u whole upon sec u and we need to write here du du now we need to integrate this with respect to du.

02:37 So we can write our function as now integration cos u and 10 square u with respect to du.

02:52 So integration we will get that is integration of cos u and we can write this sec square u minus 1 and with respect to du.

03:10 So after simplify this we will get that is we know that 1 upon cos is 1 upon sec so it becomes integration of sec u with respect to du minus integration of cos u with respect to d...

Question

Determine $L^{-1}\{F\}$. $s^2F(s) - 4sF(s) - 12F(s) = \frac{3s^2 + 2}{s^2 + 3s}$ $L^{-1}\{F\} = $

Question

Determine $L^{-1}\{F\}$. $s^2F(s) - 4sF(s) - 12F(s) = \frac{3s^2 + 2}{s^2 + 3s}$ $L^{-1}\{F\} = $

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