en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of csc(x)

Solution

integral

csc (x)

Solution

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

Solution steps

\int csc (x) d x

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 = tan (\frac{x}{2})

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

Add a constant to the solution

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

Popular Examples

integral of (sqrt(x)+sqrt(2))/(sqrt(2x))

\int \frac{x + 2}{2 x} d x

integral of 6sec^2(6x)tan(6x)

\int 6 sec^{2} (6 x) tan (6 x) d x

integral of 1/(cos^2(x)(1+tan(x)))

\int \frac{1}{cos ^{2} ( x ) ( 1 + tan ( x ) )} d x

integral of (x^2)/((x+1)^{10)}

\int \frac{x ^{2}}{( x + 1 ) ^{10}} d x

integral of-2x^2e^{x^3}

\int - 2 x^{2} e^{x^{3}} d x

Frequently Asked Questions (FAQ)

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