What is the solution for (dy)/(dx)=arctan(-6x) ?

The solution for (dy)/(dx)=arctan(-6x) is y=xarctan(-6x)+1/12 ln(36x^2+1)+c_{1}

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(dy)/(dx)=arctan(-6x)

\frac{d y}{d x} = arctan (- 6 x)

y = x arctan (- 6 x) + \frac{1}{12} ln (36 x^{2} + 1) + c_{1}

Solution steps

\frac{d y}{d x} = arctan (- 6 x)

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = arctan (- 6 x)

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int arctan (- 6 x) d x

\int arctan (- 6 x) d x = x arctan (- 6 x) + \frac{1}{12} ln (36 x^{2} + 1) + c_{1}

y = x arctan (- 6 x) + \frac{1}{12} ln (36 x^{2} + 1) + c_{1}

y = (\frac{2 x + 1}{3 x - 1})^{4}

\int e^{- 6 x} d x

n = 1 \sum \infty (x - 3)^{n}

x \to 1 lim (\frac{4}{x - 1})

\frac{d ^{2}}{d x ^{2}} (2 x^{3})

What is the solution for (dy)/(dx)=arctan(-6x) ?
The solution for (dy)/(dx)=arctan(-6x) is y=xarctan(-6x)+1/12 ln(36x^2+1)+c_{1}