Finding sequence of functions that integral tends to infinity.

Let $x_n(t)$ be functions from $C^1[0,\frac{3\pi}{2}]$ such as $x_n(0)=0$, $x_n(\frac{3\pi}{2})=-\frac{3\pi}{2}$

Find such functional sequence $x_n(t)$ that integral $\int\limits_0^\frac{3\pi}{2}(x^2(t) -4x(t)\cos(t)- x'(t)^2)dt\rightarrow + \infty$ and
$\int\limits_0^\frac{3\pi}{2}(x^2(t) -4x(t)\cos(t)- x'(t)^2)dt\rightarrow - \infty$

Comment: Actually functions must not be from $C^1[0,\frac{3\pi}{2}]$ but they must be approximated with $C^1[0,\frac{3\pi}{2}]$ functions.

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How can the integral converge $\to+\infty$ and $\to-\infty$ at the same time? –  Hagen von Eitzen Dec 19 '12 at 17:19