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

The integral of xcsc^2(4x) is -1/4 xcot(4x)+1/16 ln|sin(4x)|+C

integral of xcsc^2(4x)

\int x csc^{2} (4 x) d x

- \frac{1}{4} x cot (4 x) + \frac{1}{16} ln ∣ sin (4 x) ∣ + C

Solution steps

\int x csc^{2} (4 x) d x

Apply Integration By Parts

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

\int - \frac{1}{4} cot (4 x) d x = - \frac{1}{16} ln ∣ sin (4 x) ∣

= - \frac{1}{4} x cot (4 x) - (- \frac{1}{16} ln ∣ sin (4 x) ∣)

Simplify

= - \frac{1}{4} x cot (4 x) + \frac{1}{16} ln ∣ sin (4 x) ∣

Add a constant to the solution

= - \frac{1}{4} x cot (4 x) + \frac{1}{16} ln ∣ sin (4 x) ∣ + C

\int_{- 1}^{1} 0.09375 (4 - x^{2}) d x

\int 24 x (6 - x^{2})^{\frac{1}{3}} d x

d er i v a t i v e \frac{c}{x} + \frac{2 a}{x ^{3}} + 8

\frac{d}{d x} (\frac{1 + csc ( x ^{9} )}{1 - cot ( x ^{9} )})

\frac{\partial}{\partial y} (ln (2 w^{3} - 7 y + 3 x y^{2}))

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