Solve ∫ 2dt/t^2=2/t+c

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

Solve for c

$$c=-\frac{4}{t}+С$$

$$t\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by t.

$$t\int \frac{2}{t^{2}}\mathrm{d}t=2+tc$$

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

$$2+tc=t\int \frac{2}{t^{2}}\mathrm{d}t$$

Subtract 2 from both sides.

$$tc=t\int \frac{2}{t^{2}}\mathrm{d}t-2$$

The equation is in standard form.

$$tc=Сt-4$$

Divide both sides by t.

$$\frac{tc}{t}=\frac{Сt-4}{t}$$

Dividing by t undoes the multiplication by t.

$$c=\frac{Сt-4}{t}$$

Divide -4+Сt by t.

$$c=-\frac{4}{t}+С$$

Solve for t

$$t=\frac{4}{С-c}$$

$$c\neq С$$