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If f(x)=|[[sinx+sin2x+sin3x,sin2x,sin3x]...

If `f(x)=|[[sinx+sin2x+sin3x,sin2x,sin3x],[3+4sinx,3,4sinx],[1+sinx,sinx,1]]|`then what is the value of `int_0^(pi/2)f(x)dx`?

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