THE NATURAL LOGARITHMIC FUNCTION: INTEGRATION Section 5.2

When you are done with your homework, you should be able to… Use the Log Rule for Integration to integrate a rational function Integrate trigonometric functions

Warm-up: Evaluate the integral.

Consider the following integral: What value of p is excluded from the general power rule? -1.0 0.0

Thales lived in 600 BC. He is famous for being the first person to… …use deduction in mathematics. …measure the size of the earth. …characterize the conic sections. All of the above.

Theorem: LOG RULE FOR INTEGRATION Let u be a differentiable function of x. 1. 2.

Integrate.

Integrate. Both A and C.

Guidelines For Integration Learn a basic list of integration formulas. Find an integration formula that resembles all or part of the integrand, and, by trial and error, find a choice of that will make the integrand conform to the formula. If you cannot find a u-substitution that works, try altering the integrand. You might try a trigonometric identity, multiplication and division by the same quantity, or addition and subtraction of the same quantity.

Integrate. Unable to evaluate with our current skills.

integrals of the six basic trigonometric functions 1. 2. 3. 4. 5. 6.

Derivation of the Cosecant Formula

Integrate. Both A and B.