What is the integral of 5csc(x) ?

The integral of 5csc(x) is 5ln|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 5csc(x)

\int 5 csc (x) d x

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

Solution steps

\int 5 csc (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int csc (x) d x

Apply u-substitution

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

= 5 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 5 ln ∣ u ∣

Substitute back

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

= 5 ln tan (\frac{x}{2})

Add a constant to the solution

= 5 ln tan (\frac{x}{2}) + C

x \to 1 + lim (\frac{x}{x - 1})

\frac{\partial}{\partial x} (l sin (θ))

n = 1 \sum \infty \frac{7 x ^{n}}{n ^{8}}

\frac{( cos ^{3} ( x ) - 1 )}{cos ^{2} ( x )}