What is the integral of tan^2(x/2) ?

The integral of tan^2(x/2) is -x+2tan(x/2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of tan^2(x/2)

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

- x + 2 tan (\frac{x}{2}) + C

Solution steps

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

Rewrite using trig identities

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

\int 1 d x = x

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

= - x + 2 tan (\frac{x}{2})

Add a constant to the solution

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

h (- x) = \frac{x ^{2} + 9}{10}

\frac{d}{d x} ((sin (x) - cos (x))^{2})

\int e^{7 x} sin (6 x) d x

y = \frac{1}{t} + \frac{1}{t ^{2}} - \frac{1}{t}

(x^{2} + a^{2})^{e^{x^{2}}}

What is the integral of tan^2(x/2) ?
The integral of tan^2(x/2) is -x+2tan(x/2)+C