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

The integral of xtan^2(x/2) is -x^2+2xtan(x/2)+(x^2)/2+4ln|cos(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 xtan^2(x/2)

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

- x^{2} + 2 x tan (\frac{x}{2}) + \frac{x ^{2}}{2} + 4 ln cos (\frac{x}{2}) + C

Solution steps

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

Apply Integration By Parts

: x (- x + 2 tan (\frac{x}{2})) - \int - x + 2 tan (\frac{x}{2}) d x

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

\int - x + 2 tan (\frac{x}{2}) d x = - \frac{x ^{2}}{2} - 4 ln cos (\frac{x}{2})

= x (- x + 2 tan (\frac{x}{2})) - (- \frac{x ^{2}}{2} - 4 ln cos (\frac{x}{2}))

Simplify

x (- x + 2 tan (\frac{x}{2})) - (- \frac{x ^{2}}{2} - 4 ln cos (\frac{x}{2})) : - x^{2} + 2 x tan (\frac{x}{2}) + \frac{x ^{2}}{2} + 4 ln cos (\frac{x}{2})

= - x^{2} + 2 x tan (\frac{x}{2}) + \frac{x ^{2}}{2} + 4 ln cos (\frac{x}{2})

Add a constant to the solution

= - x^{2} + 2 x tan (\frac{x}{2}) + \frac{x ^{2}}{2} + 4 ln cos (\frac{x}{2}) + C

\int - tan (x) cos (x) d x

\int \frac{4 x}{x ^{2}} d x

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

\int 3 x^{2} + 4 x - 7 d x

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

What is the integral of xtan^2(x/2) ?
The integral of xtan^2(x/2) is -x^2+2xtan(x/2)+(x^2)/2+4ln|cos(x/2)|+C