Math 141, Spring 2016, Assignment 2

By one of those caprices of the mind, which we are perhaps most subject to in early youth, I at once gave up my former occupations; set down natural history and all its progeny as a deformed and abortive creation; and entertained the greatest disdain for a would-be science, which could never even step within the threshold of real knowledge. In this mood of mind I betook myself to the mathematics, and the branches of study appertaining to that science, as being built upon secure foundations, and so, worthy of my consideration.

- Mary Shelley, Frankenstein

State the following formulas:

1. Formula for $\int\tan^{-1}(x)\,dx$.
2. Formula for $\int\sec(x)\,dx$.
3. Product-to-sum identities (these appear at the top of page 290).

Study the following summaries from the textbook:

1. Key Idea 11, page 286.
2. Key idea 12, page 291.

Solve the following problems:

1. Section 6.2, problems 5, 7, 13, 19, 21, 25, 35, and 39.
2. Section 6.3, problems 5, 7, 10, 11, 19, 21, 23, 25, and 27.

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