What is the integral of (sec(y))/(cotan(y)) ?

The integral of (sec(y))/(cotan(y)) is 1/(co)ln|tan(y/2)|+C

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integral of (sec(y))/(cotan(y))

\int \frac{sec ( y )}{co tan ( y )} d y

\frac{1}{co} ln tan (\frac{y}{2}) + C

Solution steps

\int \frac{sec ( y )}{co tan ( y )} d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{co} \cdot \int \frac{sec ( y )}{tan ( y )} d y

Apply u-substitution

= \frac{1}{co} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{co} ln ∣ u ∣

Substitute back

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

= \frac{1}{co} ln tan (\frac{y}{2})

Add a constant to the solution

= \frac{1}{co} ln tan (\frac{y}{2}) + C

What is the integral of (sec(y))/(cotan(y)) ?
The integral of (sec(y))/(cotan(y)) is 1/(co)ln|tan(y/2)|+C