What is the integral of (1-cot^2(x)) ?

The integral of (1-cot^2(x)) is 2x+cot(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-cot^2(x))

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

2 x + cot (x) + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 1 d x = x

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

= x - (- x - cot (x))

Simplify

= 2 x + cot (x)

Add a constant to the solution

= 2 x + cot (x) + C

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

\int \frac{7 ( tan ( x ) ) ^{2}}{sec ( x )} d x

\int y x^{2} + y^{2} - 2 x d y

\int arccot (3 y) d y

\int 36 x^{2} + 12 x + 10 d x

What is the integral of (1-cot^2(x)) ?
The integral of (1-cot^2(x)) is 2x+cot(x)+C