What is the integral of 1/3 csc(x)cot(x) ?

The integral of 1/3 csc(x)cot(x) is -1/3 csc(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/3 csc(x)cot(x)

\int \frac{1}{3} csc (x) cot (x) d x

- \frac{1}{3} csc (x) + C

Solution steps

\int \frac{1}{3} csc (x) cot (x) d x

Take the constant out:

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

= \frac{1}{3} \cdot \int csc (x) cot (x) d x

Apply u-substitution

: \int - 1 d u

= \frac{1}{3} \cdot \int - 1 d u

Integral of a constant:

\int a d x = a x

= \frac{1}{3} (- 1) u

Substitute back

u = csc (x)

= \frac{1}{3} (- 1) csc (x)

Simplify

= - \frac{1}{3} csc (x)

Add a constant to the solution

= - \frac{1}{3} csc (x) + C

\int \frac{( x - 2 ) ^{2} - 16}{x - 2} d x

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

\int sin^{2} (φ) cos^{6} (φ) d φ

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

\int \frac{2}{9} x e^{- (\frac{x}{3})^{2}} d x

What is the integral of 1/3 csc(x)cot(x) ?
The integral of 1/3 csc(x)cot(x) is -1/3 csc(x)+C