Solve ∫ f(x) wrt x=f(x)dx

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

Solve for d

$$\left\{\begin{matrix}d=\frac{1}{2}+\frac{С}{2fx^{2}}\text{, }&x\neq 0\text{ and }f\neq 0\\d\in \mathrm{R}\text{, }&\left(x=0\text{ or }f=0\right)\text{ and }С=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$\int fx\mathrm{d}x=fx^{2}d$$

Swap sides so that all variable terms are on the left hand side.

$$fx^{2}d=\int fx\mathrm{d}x$$

The equation is in standard form.

$$fx^{2}d=\frac{fx^{2}}{2}+С$$

Divide both sides by x^{2}f.

$$\frac{fx^{2}d}{fx^{2}}=\frac{\frac{fx^{2}}{2}+С}{fx^{2}}$$

Dividing by x^{2}f undoes the multiplication by x^{2}f.

$$d=\frac{\frac{fx^{2}}{2}+С}{fx^{2}}$$

Divide \frac{fx^{2}}{2}+С by x^{2}f.

$$d=\frac{1}{2}+\frac{С}{fx^{2}}$$

Solve for f

$$\left\{\begin{matrix}f=\frac{С}{\left(1-d\right)x^{2}}\text{, }&d\neq 1\text{ and }x\neq 0\\f\in \mathrm{R}\text{, }&\left(x=0\text{ or }d=1\right)\text{ and }С=0\end{matrix}\right.$$