Integration by Parts Write an integral that requires three applications of integration by parts. Explain why three applications are needed.
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What applications can you find either in your program of study or elsewhere that require integration to reach a solution?
How do we recognize an integral whose solution will be a logarithmic form? How do we solve such an integral?
How do we use the formula for the integral of ex to integrate functions of this form?
How do we use the basic trig integration formulas to integrate more complex trig functions?
What role does substitution play in integration with logarithmic, exponential, and trig forms?
Why is calculus, and in particular, integral calculus, the foundation for the study of physics? In other words, why did Sir Isaac Newton develop calculus?
CONCEPT CHECK
Using Integration by Parts How can you use integration by parts on an integrand with a single term that does not fit any of the basic integration rules?