Energy stored in coil with given relationship between current and flux

[Trip1]

Homework Statement

The relationship between the current in an N-turn coil and the flux created by it is given as:

\Phi = \frac{ai}{b+ci}

Determine the energy stored in the coil when the current varies from 0 to I.

Homework Equations

W = N \int{i d\Phi}

The Attempt at a Solution

Started by differentiating the given relationship with respect to i, using the quotient rule

\frac{d\Phi}{di} = \frac{a(b+ci) - cai}{(b+c{i}^2)} \\ \\<br /> \Rightarrow d\Phi = \frac{a(b+ci)}{{(b+ci}^2)}di - \frac{aci}{(b+ci)^2}di<br /> <br />

I then proceed to substitute this expression for d\Phi into the equation for W above, and setup two integrals (one for each term), integrating with respect to i from 0 to I.

Problem is, the integrations are very complex to do by hand, and they aren't in a general form to lookup in a table. This leads me to believe I've made a mistake somewhere, but i can't seem to find it.

Any help would be greatly appreciated, thanks.

 

[TSny]

Homework Equations

W = N \int{i d\Phi}
.

You might try integration by parts.