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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cos(u))/(sin(u))

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

ln ∣ sin (u) ∣ + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

v = sin (u)

= ln ∣ sin (u) ∣

Add a constant to the solution

= ln ∣ sin (u) ∣ + C

\int \frac{2}{3 6 x} d x

\int \frac{3 x}{1 + x ^{4}} d x

\int 1 - tan (x) d x

\int \frac{x ^{3}}{( 5 x ^{4} + 2 ) ^{3}} d x

\int (8 + 5^{x}) d x

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