What is the integral of x+2/(sin(x)) ?

The integral of x+2/(sin(x)) is (x^2)/2+2ln|tan(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 x+2/(sin(x))

\int x + \frac{2}{sin ( x )} d x

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

Solution steps

\int x + \frac{2}{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 x d x + \int \frac{2}{sin ( x )} d x

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

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

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

Add a constant to the solution

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

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

\int (x + 1)^{3} (x - 2) d x

\int \frac{1}{x} 25 - x^{2} d x

\int \frac{( 3 x ^{4} - 3 x ^{2} + x )}{x} d x

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