What is the integral of sec(4x)-csc((2x)/3) ?

The integral of sec(4x)-csc((2x)/3) is 1/4 ln|tan(4x)+sec(4x)|-3/2 ln|tan(x/3)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sec(4x)-csc((2x)/3)

\int sec (4 x) - csc (\frac{2 x}{3}) d x

\frac{1}{4} ln ∣ tan (4 x) + sec (4 x) ∣ - \frac{3}{2} ln tan (\frac{x}{3}) + C

Solution steps

\int sec (4 x) - csc (\frac{2 x}{3}) 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 sec (4 x) d x - \int csc (\frac{2 x}{3}) d x

\int sec (4 x) d x = \frac{1}{4} ln ∣ tan (4 x) + sec (4 x) ∣

\int csc (\frac{2 x}{3}) d x = \frac{3}{2} ln tan (\frac{x}{3})

= \frac{1}{4} ln ∣ tan (4 x) + sec (4 x) ∣ - \frac{3}{2} ln tan (\frac{x}{3})

Add a constant to the solution

= \frac{1}{4} ln ∣ tan (4 x) + sec (4 x) ∣ - \frac{3}{2} ln tan (\frac{x}{3}) + C

\int \frac{1}{2 - 3 y} d y

\int sin (a \cdot x) \cdot sin (b \cdot x) d x

\int \frac{r}{16 - 9 r ^{2}} d r

\int \frac{100}{25 x ^{2} + 36} d x

\int sin (x) (tan (x) + cot (x)) d x

What is the integral of sec(4x)-csc((2x)/3) ?
The integral of sec(4x)-csc((2x)/3) is 1/4 ln|tan(4x)+sec(4x)|-3/2 ln|tan(x/3)|+C