Find $\int \cos x\,dx$.

How we read your problem

Find the indefinite integral (antiderivative) of cos(x) with respect to x.

Step-by-step solution

1. 1

   Start with the integral

   $$\int \cos\left( x\right)\,dx$$
2. 2

   ∫ cos x dx = sin x

   $$\int \cos\left( x\right)\,dx = \sin\left( x\right)$$
3. 3

   Simplify and add the constant of integration

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

Formulas used

• Power rule

  $$\int x^n\,dx = \frac{x^{n+1}}{n+1} + C,\ n \neq -1$$

An antiderivative F satisfies F′(x) = f(x). Because the derivative of any constant is 0, every antiderivative differs by a constant C.

Verification

• Differentiated the answer and compared it with the integrand at 8 sample points ✓