What is the integral of (sec(3x))/(cot(3x)) ?

The integral of (sec(3x))/(cot(3x)) is 1/3 sec(3x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sec(3x))/(cot(3x))

\int \frac{sec ( 3 x )}{cot ( 3 x )} d x

\frac{1}{3} sec (3 x) + C

Solution steps

\int \frac{sec ( 3 x )}{cot ( 3 x )} d x

Rewrite using trig identities

= \int sec (3 x) tan (3 x) d x

Apply u-substitution

: \int \frac{1}{3} d u

= \int \frac{1}{3} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{3} u

Substitute back

u = sec (3 x)

= \frac{1}{3} sec (3 x)

Add a constant to the solution

= \frac{1}{3} sec (3 x) + C

\frac{\partial}{\partial y} (\frac{y}{2 x + 3 y})

\int_{0}^{2 π} (cos (x))^{2} d x

\frac{2 x ^{2} + 6 x + 2}{x}

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

(\frac{1}{x} + 2 y^{2} x) d x + (2 y x^{2} - cos (y)) d y = 0, y (1) = π

What is the integral of (sec(3x))/(cot(3x)) ?
The integral of (sec(3x))/(cot(3x)) is 1/3 sec(3x)+C