009B Sample Final 2, Problem 6

Evaluate the following integrals:

(a) $\int {\frac {dx}{x^{2}{\sqrt {x^{2}-16}}}}$

(b) $\int _{-\pi }^{\pi }\sin ^{3}x\cos ^{3}x~dx$

(c) $\int _{0}^{1}{\frac {x-3}{x^{2}+6x+5}}~dx$

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

Final Answer:
(a)
(b)
(c)

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