en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of csc(u)

Solution

\int csc (u) d u

Solution

ln tan (\frac{u}{2}) + C

Solution steps

\int csc (u) d u

Apply u-substitution

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

v = tan (\frac{u}{2})

= ln tan (\frac{u}{2})

Add a constant to the solution

= ln tan (\frac{u}{2}) + C

Graph

Popular Examples

derivative of (-y/(x^2+y^2))

integral of 5\sqrt[4]{e^x}

integral of (x^2+48x-16)/(x^3-16x)

derivative of 2^x+1

Frequently Asked Questions (FAQ)

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