What is the integral of cos(x)cot(x) ?

The integral of cos(x)cot(x) is ln|tan(x/2)|+cos(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(x)cot(x)

\int cos (x) cot (x) d x

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

Solution steps

\int cos (x) cot (x) d x

Rewrite using trig identities

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

Expand

\frac{1 - sin ^{2} ( x )}{sin ( x )} : \frac{1}{sin ( x )} - sin (x)

= \int \frac{1}{sin ( x )} - sin (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 \frac{1}{sin ( x )} d x - \int sin (x) d x

\int \frac{1}{sin ( x )} d x = ln tan (\frac{x}{2})

\int sin (x) d x = - cos (x)

= ln tan (\frac{x}{2}) - (- cos (x))

Simplify

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

Add a constant to the solution

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

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

(- 1, 0), (1, 2)

\int sec^{2} (x) e^{t a n (x)} d x

f (x) = x^{π}

x \to 1 - lim (tan (\frac{π x}{2}))

What is the integral of cos(x)cot(x) ?
The integral of cos(x)cot(x) is ln|tan(x/2)|+cos(x)+C