What is the integral of 1/(sin(x)) ?

The integral of 1/(sin(x)) is ln|tan(x/2)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(sin(x))

\int \frac{1}{sin ( x )} d x

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

Solution steps

\int \frac{1}{sin ( 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

\frac{1 - 2 t}{1 + 3 t}

f (x) = x^{2} + 10 x + 242 x + 8

\int 3 (e^{3 x} - e^{x}) d x

\int (\frac{1}{x ^{13}}) d x

\frac{d}{d x} (x^{2} sin^{8} (x) + x cos^{- 5} (x))

What is the integral of 1/(sin(x)) ?
The integral of 1/(sin(x)) is ln|tan(x/2)|+C