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Integral of cos x

∫cos⁡(x) dx=sin⁡(x)+C\int \cos\left(x\right)\,dx = \sin\left(x\right) + C

The derivative of sin x is cos x, so ∫cos x dx = sin x + C.

Step by step

  1. Trig rule

    ∫cos u du = sin u.

    ∫cos⁡(x) dx=sin⁡(x)\int \cos\left(x\right)\,dx = \sin\left(x\right)
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  • f(x) = cos x
  • F(x) + C

Every choice of C gives a valid antiderivative, since shifting up or down doesn’t change the slope.

Open in the integral calculator

Questions students ask

What is the integral of cos x?

∫cos⁡(x) dx=sin⁡(x)+C\int \cos\left(x\right)\,dx = \sin\left(x\right) + C.

How do you integrate cos x?

The derivative of sin x is cos x, so ∫cos x dx = sin x + C.

How can I check the answer?

Differentiate it: the derivative of sin⁡(x)\sin\left(x\right) is cos⁡(x)\cos\left(x\right). CalcViz checks every antiderivative this way before showing it.