Integrating Exponential Functions TS: Making decisions after reflection and review

Objective  To evaluate the integrals of exponential and rational functions.

Exponential Functions What does ? What’s a function whose derivative is e x ? Exponential Rule of Integration

Exponential Functions

Test: Take the derivative of the choice of u. If you cannot find it elsewhere in the integrand, then use a different expression for u. Testing Zone: This expression is off only by a constant multiple.

Exponential Functions

Conclusion  Integration by substitution is a technique for finding the antiderivative of a composite function.  Experiment with different choices for u when using integration by substitution.  A good choice is one whose derivative is expressed elsewhere in the integrand.