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{\bf
  {\Large
MAT 137 (Calculus II) Sample Gateway Exam
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Suggested time: 20 minutes}
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No notes are allowed.  No calculators are allowed. No partial credit will be awarded.

Evaluate the integrals.

1. \ $\displaystyle \int_0^2 3x^2 + 4x + 5 \, dx$
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2. \ $\displaystyle \int \frac{2}{1 + x^2} \, dx$
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3. \ $\displaystyle \int \frac{3x^2 - 1}{x^3} \, dx$
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4.\ $\displaystyle \int x e^{x^2} \, dx$
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5.\ $\displaystyle \int x \sin(2x) \, dx$
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6. \ $\displaystyle \int \frac{1}{x(x-1)} \, dx$
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7. \ $\displaystyle \int \ln(x) \, dx$
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8. \ $\displaystyle \int \frac{\cos(x)}{4 - \sin(x)} \, dx$
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