What is the integral of cot(49x) ?

The integral of cot(49x) is 1/49 ln|sin(49x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cot(49x)

\int cot (49 x) d x

\frac{1}{49} ln ∣ sin (49 x) ∣ + C

Solution steps

\int cot (49 x) d x

Rewrite using trig identities

= \int \frac{cos ( 49 x )}{sin ( 49 x )} d x

Apply u-substitution

: \int \frac{1}{49 u} d u

= \int \frac{1}{49 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{49} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{49} ln ∣ u ∣

Substitute back

u = sin (49 x)

= \frac{1}{49} ln ∣ sin (49 x) ∣

Add a constant to the solution

= \frac{1}{49} ln ∣ sin (49 x) ∣ + C

\int \frac{8 cos ( 5 x )}{3} d x

\int - 15 x^{2} d x

\int t e^{6 t^{2}} d t

\int y y - 1 d y

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

What is the integral of cot(49x) ?
The integral of cot(49x) is 1/49 ln|sin(49x)|+C