Who's up to the challenge? 5

Calculus Level 4

01x2cosxsinxdx \large \int_0^1 x^2 \cos x \sin x \, dx

If the integral above is in the form of

A+BsinCDcosCE, \dfrac {-A + B\sin C - D\cos C}E ,

where A,B,C,DA,B,C,D and EE are positive integers, find the minimum value of A+B+C+D+EA+B+C+D+E.

Clarification: Angles are measured in radians.


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