Form Factor - Simply take the real part?

[unscientific]

Homework Statement

Show that the Form factor is $\frac{3(sin x - x cos x)}{x^3}$.

Homework Equations

The Attempt at a Solution

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I know that the form factor is simply the Fourier transform of the normalized charge density:
F(q) = \int \frac{\rho}{Z} e^{-i (\Delta \vec k) \cdot \vec r} d^3 r
= \int_0^R \left( \frac{\rho_0}{\frac{4}{3} \pi R^3 \rho_0} \right) e^{i \left( \frac{ q}{\hbar}\right) r} \cdot 4 \pi r^2 dr
= \frac{3}{R^3} \int_0^R r^2 e^{-i \left( \frac{q}{\hbar} \right) r} dr

Do I simply take the real part of this integral? Or do I have to do some form of complex/contour integration?

I tried taking only the real part, which gave the wrong asnwer: $F(q) = \frac{3\left(x^2 sin (x) - 2x cos(x) - 2 sin (x) \right)}{x^3}$.

 

[unscientific]

Solved it.