What is the solution for (dx)/(dt)= 1/(t(1-t)) ?

The solution for (dx)/(dt)= 1/(t(1-t)) is x=ln(t)-ln(t-1)+c_{1}

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(dx)/(dt)= 1/(t(1-t))

\frac{d x}{d t} = \frac{1}{t ( 1 - t )}

x = ln (t) - ln (t - 1) + c_{1}

Solution steps

\frac{d x}{d t} = \frac{1}{t ( 1 - t )}

Substitute

\frac{d x}{d t}

with

x^{'} (t)

x^{^{'}} (t) = \frac{1}{t ( 1 - t )}

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

then

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

x = \int \frac{1}{t ( 1 - t )} d t

\int \frac{1}{t ( 1 - t )} d t = ln (t) - ln (t - 1) + c_{1}

x = ln (t) - ln (t - 1) + c_{1}

\frac{d}{d t} (x y)

7 x sin (π x)

\int (x - \frac{1}{x ^{2}}) d x

\int ln (5^{x}) d x

9 t^{2} + t^{3}

What is the solution for (dx)/(dt)= 1/(t(1-t)) ?
The solution for (dx)/(dt)= 1/(t(1-t)) is x=ln(t)-ln(t-1)+c_{1}