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Integration by Substitution

AP Calculus AB· difficulty 2/5

∫cos⁡(3x) dx=\displaystyle\int \cos(3x)\,dx =

  • A

    3sin⁡(3x)+C3\sin(3x) + C

  • B

    sin⁡(3x)+C\sin(3x) + C

  • C

    −sin⁡(3x)/3+C-\sin(3x)/3 + C

  • D

    sin⁡(3x)3+C\dfrac{\sin(3x)}{3} + C

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Explanation

u=3xu = 3x, du=3 dxdu = 3\,dx. ∫cos⁡u du/3=sin⁡u/3\int \cos u\,du/3 = \sin u/3.

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