What is the solution for (dy)/(dx)=6x(x-3) ?

The solution for (dy)/(dx)=6x(x-3) is y=6((x^3)/3-(3x^2)/2)+c_{1}

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(dy)/(dx)=6x(x-3)

\frac{d y}{d x} = 6 x (x - 3)

y = 6 (\frac{x ^{3}}{3} - \frac{3 x ^{2}}{2}) + c_{1}

Solution steps

\frac{d y}{d x} = 6 x (x - 3)

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 6 x (x - 3)

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

then

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

y = \int 6 x (x - 3) d x

\int 6 x (x - 3) d x = 6 (\frac{x ^{3}}{3} - \frac{3 x ^{2}}{2}) + c_{1}

y = 6 (\frac{x ^{3}}{3} - \frac{3 x ^{2}}{2}) + c_{1}

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

4 x - 8

9 - 4 x, at x = - 1

\int_{1}^{4} - 4 e^{x} d x

\frac{d}{d x} (\frac{x - 8}{7 x ^{2} e ^{x}})

What is the solution for (dy)/(dx)=6x(x-3) ?
The solution for (dy)/(dx)=6x(x-3) is y=6((x^3)/3-(3x^2)/2)+c_{1}