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Find the indefinite integral of the function ((2x) - (2x)).

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السؤال 74:
المطلوب هو إيجاد التكامل غير المحدد للدالة (cos⁡(2x)−sin⁡(2x))(\cos(2x) - \sin(2x)).
∫(cos⁡(2x)−sin⁡(2x)) dx\int (\cos(2x) - \sin(2x))\,dx

  1. نكامل كل حد على حدة.

    تكامل cos⁡(2x)\cos(2x) هو 12sin⁡(2x)\frac{1}{2}\sin(2x).
    تكامل −sin⁡(2x)-\sin(2x) هو −(−12cos⁡(2x))=12cos⁡(2x)- (-\frac{1}{2}\cos(2x)) = \frac{1}{2}\cos(2x).

  2. نجمع النتائج.

    ∫(cos⁡(2x)−sin⁡(2x)) dx=12sin⁡(2x)+12cos⁡(2x)+C\int (\cos(2x) - \sin(2x))\,dx = \frac{1}{2}\sin(2x) + \frac{1}{2}\cos(2x) + C

    بمراجعة الخيارات، لا يوجد خيار يطابق هذه النتيجة تمامًا

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