Given the derivative of some integrable function f(x) is .

    (b)    Find .

Difficulty Rating: 

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Solution:

(a)    To find f(x), you need to integrate f ':

We know that f(1) = e, so if you plug in 1 for x, the result should be e:

This gives you the exact value of C, so the final answer is .
(b)    In order to calculate , you need to use the following formula (which you should have memorized):

In order to calculate f ^-1(3), find the place that f(x) = 3. Then, complete your calculations.

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Calculus II (BC): A Delightful Assortment of Intregrals Find the following antiderivatives:

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Solution:

(a)    You need to use Integration by Parts twice to get this problem correct. (b)    This is a partial fractions problem.