What is the integral of 1/(y(100-y)) ?

The integral of 1/(y(100-y)) is 1/100 ln|y|-1/100 ln|y-100|+C

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integral of 1/(y(100-y))

\int \frac{1}{y ( 100 - y )} d y

\frac{1}{100} ln ∣ y ∣ - \frac{1}{100} ln ∣ y - 100 ∣ + C

Solution steps

\int \frac{1}{y ( 100 - y )} d y

Take the partial fraction of

\frac{1}{y ( 100 - y )} : \frac{1}{100 y} - \frac{1}{100 ( y - 100 )}

= \int \frac{1}{100 y} - \frac{1}{100 ( y - 100 )} d y

Apply the Sum Rule:

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

= \int \frac{1}{100 y} d y - \int \frac{1}{100 ( y - 100 )} d y

\int \frac{1}{100 y} d y = \frac{1}{100} ln ∣ y ∣

\int \frac{1}{100 ( y - 100 )} d y = \frac{1}{100} ln ∣ y - 100 ∣

= \frac{1}{100} ln ∣ y ∣ - \frac{1}{100} ln ∣ y - 100 ∣

Add a constant to the solution

= \frac{1}{100} ln ∣ y ∣ - \frac{1}{100} ln ∣ y - 100 ∣ + C

x \to 0 + lim (\frac{1}{1 - e ^{x}})

(\frac{2 x - 7}{2 + 3 x})

\frac{1}{s ^{2} ( s - 1 ) ^{2}}

\int (\frac{x}{2}) d x

\int \frac{6 x}{( x ^{2} + 7 ) ^{2}} d x

What is the integral of 1/(y(100-y)) ?
The integral of 1/(y(100-y)) is 1/100 ln|y|-1/100 ln|y-100|+C