What is the solution for (df)/(ds)=12s+(5s)/(sqrt(9-s^2)) ?

The solution for (df)/(ds)=12s+(5s)/(sqrt(9-s^2)) is f(s)=6s^2-5sqrt(9-s^2)+c_{1}

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(df)/(ds)=12s+(5s)/(sqrt(9-s^2))

\frac{df}{d s} = 12 s + \frac{5 s}{9 - s ^{2}}

f (s) = 6 s^{2} - 5 9 - s^{2} + c_{1}

Solution steps

\frac{df}{d s} = 12 s + \frac{5 s}{9 - s ^{2}}

Substitute

\frac{df}{d s}

with

f^{'} (s)

f^{^{'}} (s) = 12 s + \frac{5 s}{9 - s ^{2}}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

f (s) = \int 12 s + \frac{5 s}{9 - s ^{2}} d s

\int 12 s + \frac{5 s}{9 - s ^{2}} d s = 6 s^{2} - 5 9 - s^{2} + c_{1}

f (s) = 6 s^{2} - 5 9 - s^{2} + c_{1}

x \to 0 lim (x^{n})

y = x^{3} cos (x)

\int_{0}^{2} (\frac{x + 2}{x - 4}) d x

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What is the solution for (df)/(ds)=12s+(5s)/(sqrt(9-s^2)) ?
The solution for (df)/(ds)=12s+(5s)/(sqrt(9-s^2)) is f(s)=6s^2-5sqrt(9-s^2)+c_{1}