To find \(y\), integrate:

\(y=\int 2x\,dx\)

Increase the power of \(x\) by 1 and divide by the new power:

\(y=\dfrac{2x^2}{2}+C=x^2+C\).

Integrate:

\(y=\int x^7\,dx\)

Increase the power by 1:

\(y=\dfrac{x^8}{8}+C\).

Integrate:

\(y=\int 3x^2\,dx\)

\(y=3\cdot\dfrac{x^3}{3}+C=x^3+C\).

Integrate the constant:

\(y=\int -15\,dx=-15x+C\).

Integrate term by term:

\(y=\int (x-x^3)\,dx\)

\(y=\int x\,dx-\int x^3\,dx\)

\(y=\dfrac{x^2}{2}-\dfrac{x^4}{4}+C\).