What is the integral of (sin(3x))/(csc^2(4x)) ?

The integral of (sin(3x))/(csc^2(4x)) is -1/3 sin^2(4x)cos(3x)+2/165 (-5cos(11x)-11cos(5x))+C

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integral of (sin(3x))/(csc^2(4x))

\int \frac{sin ( 3 x )}{csc ^{2} ( 4 x )} d x

- \frac{1}{3} sin^{2} (4 x) cos (3 x) + \frac{2}{165} (- 5 cos (11 x) - 11 cos (5 x)) + C

Solution steps

\int \frac{sin ( 3 x )}{csc ^{2} ( 4 x )} d x

Apply Integration By Parts

: - \frac{1}{3} sin^{2} (4 x) cos (3 x) - \int - \frac{4}{3} sin (8 x) cos (3 x) d x

= - \frac{1}{3} sin^{2} (4 x) cos (3 x) - \int - \frac{4}{3} sin (8 x) cos (3 x) d x

\int - \frac{4}{3} sin (8 x) cos (3 x) d x = - \frac{2}{165} (- 5 cos (11 x) - 11 cos (5 x))

= - \frac{1}{3} sin^{2} (4 x) cos (3 x) - (- \frac{2}{165} (- 5 cos (11 x) - 11 cos (5 x)))

Simplify

= - \frac{1}{3} sin^{2} (4 x) cos (3 x) + \frac{2}{165} (- 5 cos (11 x) - 11 cos (5 x))

Add a constant to the solution

= - \frac{1}{3} sin^{2} (4 x) cos (3 x) + \frac{2}{165} (- 5 cos (11 x) - 11 cos (5 x)) + C

\frac{d y}{d x} = \frac{1 - y}{1 - x}

\frac{\partial}{\partial v} (2 v sin (u))

\frac{1}{s ^{2} - s}

x \to \frac{1}{5} lim (\frac{x}{10 x - 2})

\frac{d}{d x} ((cos (x))^{3})

What is the integral of (sin(3x))/(csc^2(4x)) ?
The integral of (sin(3x))/(csc^2(4x)) is -1/3 sin^2(4x)cos(3x)+2/165 (-5cos(11x)-11cos(5x))+C