Solve ∫ 2my^2/x^3 wrt x

$$\int \frac { 2 m y ^ { 2 } } { x ^ { 3 } } d x$$

Evaluate

$$-\left(\frac{y}{x}\right)^{2}m+С$$

Solution Steps

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$2my^{2}\int \frac{1}{x^{3}}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int \frac{1}{x^{3}}\mathrm{d}x with -\frac{1}{2x^{2}}.

$$2my^{2}\left(-\frac{1}{2x^{2}}\right)$$

Simplify.

$$-\frac{my^{2}}{x^{2}}$$

If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$-\frac{my^{2}}{x^{2}}+С$$

Differentiate w.r.t. x

$$\frac{2my^{2}}{x^{3}}$$