\[ \int_0^{\frac {\pi}{4}} \frac {\sin ^ 2 x}{\cos ^ 3 x}\ dx\]

If my delivery equals \( \frac ab \{\sqrt {c} - \ln (d + \sqrt {e})\}\) , a,b,c,d,e are positive integers , find \(a+b+c+d+e\) .

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