Solve ∫ (-y/x^2) wrt x

$$\int ( \frac { - y } { x ^ { 2 } } ) d x$$

Evaluate

$$\frac{y}{x}+С$$

Solution Steps

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

$$-y\int \frac{1}{x^{2}}\mathrm{d}x$$

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

$$-y\left(-\frac{1}{x}\right)$$

Simplify.

$$\frac{y}{x}$$

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.

$$\frac{y}{x}+С$$

Differentiate w.r.t. x

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