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A purpose clause explains why an action is done and so can be considered the motivation behind the verb. It is constructed with 'ut' + a subjunctive verb and is translated in English as '...

Knowing that 1-2sin²(x) = cos(2x), substitute sin²(x) as: sin²(x) = (1-cos(2x))/2Use the linearity of the integral to split it into: Int(1/2) - Int(cos(2x)/2)dxWhich is in...