What is the integral of (9sin(x)+2sec(x))/(tan(x)) ?

The integral of (9sin(x)+2sec(x))/(tan(x)) is 9sin(x)+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 (9sin(x)+2sec(x))/(tan(x))

\int \frac{9 sin ( x ) + 2 sec ( x )}{tan ( x )} d x

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

Solution steps

\int \frac{9 sin ( x ) + 2 sec ( x )}{tan ( x )} d x

Expand

\frac{9 sin ( x ) + 2 sec ( x )}{tan ( x )} : \frac{9 sin ( x )}{tan ( x )} + \frac{2 sec ( x )}{tan ( x )}

= \int \frac{9 sin ( x )}{tan ( x )} + \frac{2 sec ( x )}{tan ( 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{9 sin ( x )}{tan ( x )} d x + \int \frac{2 sec ( x )}{tan ( x )} d x

\int \frac{9 sin ( x )}{tan ( x )} d x = 9 sin (x)

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

= 9 sin (x) + 2 ln tan (\frac{x}{2})

Add a constant to the solution

= 9 sin (x) + 2 ln tan (\frac{x}{2}) + C

\frac{d y}{d x} = x + 1

(x + 2 y) d x - x d y = 0

\int (3 x^{4} - 5 x^{2} + x) d x

\int_{\frac{3}{4}}^{\infty} 2 x d x

x \to 1 - lim (\frac{1}{( x - 1 ) ^{2}})

What is the integral of (9sin(x)+2sec(x))/(tan(x)) ?
The integral of (9sin(x)+2sec(x))/(tan(x)) is 9sin(x)+2ln|tan(x/2)|+C