What is the integral of 2xcsc(4x)cot(4x) ?

The integral of 2xcsc(4x)cot(4x) is 2(-1/4 xcsc(4x)+1/16 ln|tan(2x)|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2xcsc(4x)cot(4x)

\int 2 x csc (4 x) cot (4 x) d x

2 (- \frac{1}{4} x csc (4 x) + \frac{1}{16} ln ∣ tan (2 x) ∣) + C

Solution steps

\int 2 x csc (4 x) cot (4 x) d x

Take the constant out:

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

= 2 \cdot \int x csc (4 x) cot (4 x) d x

Apply Integration By Parts

: - \frac{1}{4} x csc (4 x) - \int - \frac{1}{4} csc (4 x) d x

= 2 (- \frac{1}{4} x csc (4 x) - \int - \frac{1}{4} csc (4 x) d x)

\int - \frac{1}{4} csc (4 x) d x = - \frac{1}{16} ln ∣ tan (2 x) ∣

= 2 (- \frac{1}{4} x csc (4 x) - (- \frac{1}{16} ln ∣ tan (2 x) ∣))

Simplify

= 2 (- \frac{1}{4} x csc (4 x) + \frac{1}{16} ln ∣ tan (2 x) ∣)

Add a constant to the solution

= 2 (- \frac{1}{4} x csc (4 x) + \frac{1}{16} ln ∣ tan (2 x) ∣) + C

\int \frac{5 x + 1}{( x - 1 ) ( 2 x + 1 )} d x

\int \frac{x - 4}{x ^{2} ( x + 1 )} d x

\int \frac{cos ^{5} ( 17 x )}{sin ^{3} ( 17 x )} d x

\int \frac{1}{x lo g _{5} ( x )} d x

What is the integral of 2xcsc(4x)cot(4x) ?
The integral of 2xcsc(4x)cot(4x) is 2(-1/4 xcsc(4x)+1/16 ln|tan(2x)|)+C