Solve ∫ -1/yy wrt y

$$\int - \frac { 1 } { y y } d y$$

Evaluate

$$\frac{1}{y}+С$$

Solution Steps

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

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

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

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

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

$$\frac{1}{y}$$

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

$$\frac{1}{y}+С$$

Differentiate w.r.t. y

$$-\frac{1}{y^{2}}$$