What is the integral of csc^2(8x) ?

The integral of csc^2(8x) is -1/8 cot(8x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of csc^2(8x)

\int csc^{2} (8 x) d x

- \frac{1}{8} cot (8 x) + C

Solution steps

\int csc^{2} (8 x) d x

Apply u-substitution

: \int csc^{2} (u) \frac{1}{8} d u

= \int csc^{2} (u) \frac{1}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int csc^{2} (u) d u

Use the common integral:

\int csc^{2} (u) d u = - cot (u)

= \frac{1}{8} (- cot (u))

Substitute back

u = 8 x

= \frac{1}{8} (- cot (8 x))

Simplify

= - \frac{1}{8} cot (8 x)

Add a constant to the solution

= - \frac{1}{8} cot (8 x) + C

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

\int 5 cos (π x) d x

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

\int (\frac{1}{e ^{x}} + 3^{\frac{x}{2}}) d x

\int 2 \frac{4 - x ^{2}}{x ^{8}} d x