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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cos(y))/(sin(y))

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

ln ∣ sin (y) ∣ + C

Solution steps

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

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 = sin (y)

= ln ∣ sin (y) ∣

Add a constant to the solution

= ln ∣ sin (y) ∣ + C

y = \frac{2 x}{x ^{2} + 1}

\int t^{2} (t - \frac{2}{t}) d t

y^{^{'}} = \frac{( 4 x sec ( \frac{y}{x} ) + y )}{x}

x \to - 6 lim (\frac{6}{x + 6})

y^{^{''}} + y = 8 x sin (x)

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