What is the integral of (3sin(x)+4sec(x))/(tan(x)) ?

The integral of (3sin(x)+4sec(x))/(tan(x)) is 3sin(x)+4ln|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 (3sin(x)+4sec(x))/(tan(x))

\int \frac{3 sin ( x ) + 4 sec ( x )}{tan ( x )} d x

3 sin (x) + 4 ln tan (\frac{x}{2}) + C

Solution steps

\int \frac{3 sin ( x ) + 4 sec ( x )}{tan ( x )} d x

Expand

\frac{3 sin ( x ) + 4 sec ( x )}{tan ( x )} : \frac{3 sin ( x )}{tan ( x )} + \frac{4 sec ( x )}{tan ( x )}

= \int \frac{3 sin ( x )}{tan ( x )} + \frac{4 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{3 sin ( x )}{tan ( x )} d x + \int \frac{4 sec ( x )}{tan ( x )} d x

\int \frac{3 sin ( x )}{tan ( x )} d x = 3 sin (x)

\int \frac{4 sec ( x )}{tan ( x )} d x = 4 ln tan (\frac{x}{2})

= 3 sin (x) + 4 ln tan (\frac{x}{2})

Add a constant to the solution

= 3 sin (x) + 4 ln tan (\frac{x}{2}) + C

f (x) = x^{l o g_{10} (x)}

\int \frac{x}{a x + b} d x

\int_{- 3}^{- 5} (- 5)^{- 3} d x

\frac{d}{d x} (- \frac{y ^{2}}{( x - y ) ^{2}})

2^{x^{2}}

What is the integral of (3sin(x)+4sec(x))/(tan(x)) ?
The integral of (3sin(x)+4sec(x))/(tan(x)) is 3sin(x)+4ln|tan(x/2)|+C