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

The integral of (sec(y))/(sec(y)-1) is -cot(y/2)+C

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

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

- cot (\frac{y}{2}) + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = tan (\frac{y}{2})

= - \frac{1}{tan ( \frac{y}{2} )}

Use the basic trigonometric identity:

\frac{1}{tan ( x )} = cot (x)

= - cot (\frac{y}{2})

Add a constant to the solution

= - cot (\frac{y}{2}) + C

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What is the integral of (sec(y))/(sec(y)-1) ?
The integral of (sec(y))/(sec(y)-1) is -cot(y/2)+C