Solve ∫ wrt y/2y^2

$$\int \frac { d y } { 2 y ^ { 2 } }$$

Evaluate

$$-\frac{1}{2y}+С$$

Solution Steps

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

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

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}.

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

Simplify.

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

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.

$$-\frac{1}{2y}+С$$

Differentiate w.r.t. y

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