What is the integral of xcot^2(x) ?

The integral of xcot^2(x) is -x^2-xcot(x)+(x^2)/2+ln|sin(x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of xcot^2(x)

\int x cot^{2} (x) d x

- x^{2} - x cot (x) + \frac{x ^{2}}{2} + ln ∣ sin (x) ∣ + C

Solution steps

\int x cot^{2} (x) d x

Apply Integration By Parts

: x (- x - cot (x)) - \int - x - cot (x) d x

= x (- x - cot (x)) - \int - x - cot (x) d x

\int - x - cot (x) d x = - \frac{x ^{2}}{2} - ln ∣ sin (x) ∣

= x (- x - cot (x)) - (- \frac{x ^{2}}{2} - ln ∣ sin (x) ∣)

Simplify

x (- x - cot (x)) - (- \frac{x ^{2}}{2} - ln ∣ sin (x) ∣) : - x^{2} - x cot (x) + \frac{x ^{2}}{2} + ln ∣ sin (x) ∣

= - x^{2} - x cot (x) + \frac{x ^{2}}{2} + ln ∣ sin (x) ∣

Add a constant to the solution

= - x^{2} - x cot (x) + \frac{x ^{2}}{2} + ln ∣ sin (x) ∣ + C

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

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

\int e^{x} (2^{x} - 1) d x

\int \frac{x + 3}{x + 2} d x

What is the integral of xcot^2(x) ?
The integral of xcot^2(x) is -x^2-xcot(x)+(x^2)/2+ln|sin(x)|+C