What is the integral of sec(x)cot(x) ?

The integral of sec(x)cot(x) is ln|tan(x/2)|+C

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integral of sec(x)cot(x)

\int sec (x) cot (x) d x

ln tan (\frac{x}{2}) + C

Solution steps

\int sec (x) cot (x) d x

Rewrite using trig identities

= \int \frac{1}{sin ( x )} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

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

= ln tan (\frac{x}{2})

Add a constant to the solution

= ln tan (\frac{x}{2}) + C

\int_{0}^{1} x^{4} - x d x

\int 1 - cos^{2} (θ) d θ

\frac{d}{d x} (7 x + 2)

y^{^{'}} + y = e^{- t} ln (t)

\frac{d}{d x} (\frac{ln ( x + y )}{ln ( y )})

What is the integral of sec(x)cot(x) ?
The integral of sec(x)cot(x) is ln|tan(x/2)|+C