Evaluate the following integrals.
$$a) \int{\frac{dx }{ 7+3x^2}} b) \int{\frac{x}{ \sqrt{1-4x^4}}}
c) \int{\frac{x+4 }{ x^2 +1}} d) \int{\frac{3x^2+3x+1 }{ x^3 +2x^2
+2x +1}}$$
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Tags: integration, trig-substitution, partial-fractions, inverse-trig, rational, tricks, a--a, computation, t3, c2
A hodgepodge of integrals. Good for automaticity training. (a) can be kludged into an arctan form (a la fin-de-partial-fractions), (b) is a substitution away from an arctan form, (c) is most easily done by splitting the x and the 4, and (d) is a miserable partial fractions grind. To actually do all these problems would be a fair amount of work, though each individual part is probably about a Technical Difficulty II.
– Eric Hsu 1998-08-09