Integrate the gradient:

\(y=\int(3x^2-6x+2)\,dx=x^3-3x^2+2x+c\).

Now use the point \((-2,-10)\):

\(-10=(-2)^3-3(-2)^2+2(-2)+c\)

\(-10=-8-12-4+c\)

\(-10=-24+c\)

\(c=14\).

So the equation is \(y=x^3-3x^2+2x+14\).

First expand:

\((1-2x)^2=1-4x+4x^2\).

Integrate:

\(y=\int(1-4x+4x^2)\,dx=x-2x^2+\frac{4}{3}x^3+c\).

Use the point \((1,8)\):

\(8=1-2+\frac{4}{3}+c\)

\(8=\frac{1}{3}+c\)

\(c=\frac{23}{3}\).

So \(y=x-2x^2+\frac{4}{3}x^3+\frac{23}{3}\).

Expand first:

\(x(2x+5)=2x^2+5x\).

Integrate:

\(y=\int(2x^2+5x)\,dx=\frac{2}{3}x^3+\frac{5}{2}x^2+c\).

Use \((5,-1)\):

\(-1=\frac{2}{3}(5)^3+\frac{5}{2}(5)^2+c\)

\(-1=\frac{250}{3}+\frac{125}{2}+c\)

\(-1=\frac{875}{6}+c\)

\(c=-\frac{881}{6}\).

So the equation is \(y=\frac{2}{3}x^3+\frac{5}{2}x^2-\frac{881}{6}\).

Simplify the gradient:

\(\sqrt{x}(\sqrt{x}-3)=x-3x^{1/2}\).

Integrate:

\(y=\int(x-3x^{1/2})\,dx=\frac{1}{2}x^2-2x^{3/2}+c\).

Use \((9,12)\):

\(12=\frac{1}{2}(9)^2-2(9)^{3/2}+c\)

\(12=\frac{81}{2}-54+c\)

\(12=-\frac{27}{2}+c\)

\(c=\frac{51}{2}\).

So the equation is \(y=\frac{1}{2}x^2-2x^{3/2}+\frac{51}{2}\).

Simplify the gradient:

\(\dfrac{9x^3-3x}{x}=9x^2-3\).

Integrate:

\(y=\int(9x^2-3)\,dx=3x^3-3x+c\).

Use \((-5,4)\):

\(4=3(-5)^3-3(-5)+c\)

\(4=-375+15+c\)

\(4=-360+c\)

\(c=364\).

So the equation is \(y=3x^3-3x+364\).