Calculating the Energy Stored in an Inductor The energy stored in an inductor has been derived from the following formulae; $P = iL\frac{di}{dt}$ (1) $P = \frac{dE}{dt}$ (2) Substituting eq. (1) into eq. (2). $\frac{dE}{dt} = iL\frac{di}{dt}$ (3) How do I remove the $dt$ term on both sides of the equation? Basically how do I get to the next step which is? And what should be the limits on the right hand side of the equation? $\int_0^iiLdi=\int dE$

Well, we have for an inductor:

$$\text{U}_\text{L}\left(t\right)=\text{L}\cdot\text{I}'_\text{L}\left(t\right)\tag1$$

Now, for the energy we have:

$$\text{E}_\text{L}\left(t\right)=\int\text{P}_\text{L}\left(t\right)\space\text{d}t=\int\text{U}_\text{L}\left(t\right)\cdot\text{I}_\text{L}\left(t\right)\space\text{d}t=\int\text{L}\cdot\text{I}'_\text{L}\left(t\right)\cdot\text{I}_\text{L}\left(t\right)\space\text{d}t\tag2$$

Now, substitute $\text{u}=\text{I}_\text{L}\left(t\right)$:

$$\int\text{L}\cdot\text{I}'_\text{L}\left(t\right)\cdot\text{I}_\text{L}\left(t\right)\space\text{d}t=\text{L}\int\text{u}\space\text{d}\text{u}=\text{L}\cdot\frac{\text{u}^2}{2}+\text{K}=\text{L}\cdot\frac{\text{I}_\text{L}\left(t\right)^2}{2}+\text{K}\tag3$$