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{\bf Math 166: Honors Calculus II}
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{\bf Quiz 4}\quad {\sl Feb. 17, 2000}

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\item Give the general form of the partial fraction decomposition of
  \[ \frac{x^7+x^3+1}{(x^4-1)(x^2+1)(x+1)^2} \]
(Do not solve for the constants.)

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\item Use an appropriate substitution to transform
  \[ \int\frac{1+\sin(x)}{2+\sin(x)}\,dx \]
into an integral of a rational function of~$u$.\newline
(Simplify as much as possible).

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\item  Integrate $\int \frac{x^2+4x+6}{x^3+2x^2+3x}\,dx$.

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