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.
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.