What is the integral of (sec(x))/(sin(x)) ?

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

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integral of (sec(x))/(sin(x))

\int \frac{sec ( x )}{sin ( x )} d x

ln ∣ tan (x) ∣ + C

Solution steps

\int \frac{sec ( x )}{sin ( x )} d x

Apply Trigonometric 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 (x)

= ln ∣ tan (x) ∣

Add a constant to the solution

= ln ∣ tan (x) ∣ + C

\frac{d}{d x} ((sin (3 x))^{3})

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

\frac{\partial}{\partial x} (- 5 x cos (x^{2} - 5 x y))

\frac{d ^{2}}{d x} (y) + 2 \frac{d y}{d x} + y = 0

\frac{\partial}{\partial x} (e^{- 2 z} y sin (x))

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