We use an indefinite integral to represent the most general antiderivative.

"The Integral of f(x) with respect to x" = F (x) dx = F (x) + C where the differential dx represents the variable.

The "+C" is an arbitrary constant and gives the most general antiderivative. This represents a whole family of antiderivatives.

Rules for Integrals are similar to Derivative rules.

  1. Constants factor out:

    c f (x) dx = c f (x) dx

  2. You can integrate (find the antiderivative of sums) one term at a time.

    {f (x) + g (x)} dx = f (x) dx + g (x) dx

  3. The Power Rule becomes:

Try it!

Problem 1:

Problem 2:

Problem 3:    (1 = x°)

Problem 4:

Problem 5:

To find integrals and antiderivatives, you need to think the same way you did when finding derivatives. The constants stay there. Rewrite the radicals and reciprocals in exponent form. You may always check your answer by taking its derivative.

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