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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sec(y))/(sin(y))

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

ln ∣ tan (y) ∣ + C

Solution steps

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

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 (y)

= ln ∣ tan (y) ∣

Add a constant to the solution

= ln ∣ tan (y) ∣ + C

\frac{\partial}{\partial x} (\frac{1}{x ^{2}})

\frac{2}{( - 2 s + 10 )}

\frac{d}{d x} (f (x) (x))

\frac{d}{d x} (3 x^{2} - 2 x + 7)

x \to 2 lim ((x + 2)^{6} (3 x^{2}))

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