What is the integral of (sec(θ))/(tan(θ)) ?

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

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integral of (sec(θ))/(tan(θ))

\int \frac{sec ( θ )}{tan ( θ )} d θ

ln tan (\frac{θ}{2}) + C

Solution steps

\int \frac{sec ( θ )}{tan ( θ )} d θ

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{θ}{2})

= ln tan (\frac{θ}{2})

Add a constant to the solution

= ln tan (\frac{θ}{2}) + C

\frac{d y}{d x} + x \cdot y = - x^{2}

\frac{d}{d x} (x (x - 4)^{2})

2 x^{2} + 3 x, at x = - 3

\int \frac{cos ( x )}{8 + sin ( x )} d x

x \to 0 lim ((1 + 8 x)^{\frac{3}{x}})

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