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

The integral of cot(x)cos(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 cot(x)cos(x)

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

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

Solution steps

\int cot (x) cos (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

\int_{- 2}^{2} x (4 - x^{2}) d x

\int_{0}^{π} (sin^{2} (x))^{2} d x

4 x y^{^{'}} - 20 y = x^{- 9}

\int 1 + ln (x) d x

x \to 0 + lim (\frac{1}{x} \cdot sin (x^{2}))

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