Solve d ∫ f(x) wrt x=f(x)dx

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

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&С=\frac{fx^{2}}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Subtract fx^{2}d from both sides.

$$d\int fx\mathrm{d}x-fx^{2}d=0$$

Reorder the terms.

$$d\int fx\mathrm{d}x-dfx^{2}=0$$

Combine all terms containing d.

$$\left(\int fx\mathrm{d}x-fx^{2}\right)d=0$$

The equation is in standard form.

$$\left(-\frac{fx^{2}}{2}+С\right)d=0$$

Divide 0 by С-\frac{1}{2}fx^{2}.

$$d=0$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&С=\frac{fx^{2}}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Subtract fx^{2}d from both sides.

$$d\int fx\mathrm{d}x-fx^{2}d=0$$

Reorder the terms.

$$d\int fx\mathrm{d}x-dfx^{2}=0$$

Combine all terms containing d.

$$\left(\int fx\mathrm{d}x-fx^{2}\right)d=0$$

The equation is in standard form.

$$\left(-\frac{fx^{2}}{2}+С\right)d=0$$

Divide 0 by С-\frac{1}{2}fx^{2}.

$$d=0$$

Solve for f (complex solution)

$$f\in \mathrm{C}$$

$$С=0\text{ or }d=0$$

Solve for f

$$f\in \mathrm{R}$$

$$С=0\text{ or }d=0$$