Solve ∫ x ^ 3 +3 wrt x/x^2=c

$$\frac { \int x ^ { 3 } + 3 d x } { x ^ { 2 } } = c$$

Solve for c

$$c=\frac{x^{2}}{4}+\frac{С}{x^{2}}+\frac{3}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}.

$$\int x^{3}+3\mathrm{d}x=cx^{2}$$

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

$$cx^{2}=\int x^{3}+3\mathrm{d}x$$

The equation is in standard form.

$$x^{2}c=\frac{x^{4}}{4}+3x+С$$

Divide both sides by x^{2}.

$$\frac{x^{2}c}{x^{2}}=\frac{\frac{x^{4}}{4}+3x+С}{x^{2}}$$

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

$$c=\frac{\frac{x^{4}}{4}+3x+С}{x^{2}}$$

Divide \frac{x^{4}}{4}+3x+С by x^{2}.

$$c=\frac{x^{2}}{4}+\frac{3x+С}{x^{2}}$$