Second Midterm-Practice test

Feel free to drop any comments or questions, and I will try to post here as many hints as I can. No answers, though: you need to get the solution by networking. Good luck, and enjoy these problems.

[Math Cheat Sheet T-shirt] [Engineer Cheat Sheet T-shirt]

Evaluate the following integrals:

  1. \displaystyle{\int_0^3 \frac{dx}{x-1}\, dx }
  2. \displaystyle{\int_{-\infty}^0 xe^{-x}\, dx }
  3. \displaystyle{\int \cos x \big( 1+\sin^2 x \big)\, dx }
  4. \displaystyle{\int \frac{\sin x + \sec x}{\tan x}\, dx }
  5. \displaystyle{\int_1^3 r^4 \ln r\, dr }
  6. \displaystyle{\int \frac{x-1}{x^2-4x+5}\, dx }
  7. \displaystyle{\int \sin^3 \theta \cos^5 \theta\, d\theta }
  8. \displaystyle{\int x\, \sin^2 x\, dx }
  9. \displaystyle{\int e^{x+e^x}\, dx }
  10. \displaystyle{\int e^2\, dx }
  11. \displaystyle{\int \frac{\ln x}{x \sqrt{1+ \big(\ln x \big)^2}}\, dx }
  12. \displaystyle{\int \big( 1+ \sqrt{x} \big)^8\, dx }
  1. \displaystyle{\int \ln \big( x^2-1 \big)\, dx }
  2. \displaystyle{\int \frac{3x^2-2}{x^2-2x-8}\, dx }
  3. \displaystyle{\int \frac{dx}{1+e^x} }
  4. \displaystyle{\int \sqrt{3-2x-x^2}\, dx }
  5. \displaystyle{\int \frac{1+\cot x}{4-\cot x}\, dx }
  6. \displaystyle{\int \sin 4x \cos 3x\, dx }
  7. \displaystyle{\int e^x \sqrt{1+e^x}\, dx }
  8. \displaystyle{\int \sqrt{1+e^x}\, dx }
  9. \displaystyle{\int x^5 e^{-x^3}\, dx }
  10. \displaystyle{\int \frac{1+\sin x}{1-\sin x}\, dx }
  11. \displaystyle{\int \frac{dx}{3-5\sin x}\, dx }
  12. \displaystyle{\int \frac{dx}{3\sin x - 4\cos x} }
  1. Anonymous
    September 29, 2011 at 11:58 am

    For number 23)

    Would t be substituted for x, and would the dt over (3-5sint) be multiplied with the dt next to it to make 2dt?

    Int: 2dt / (3-5sint)

    correct?

  2. Benoit
    September 29, 2011 at 11:59 am

    23)

    Int: 2dt / [3 – 5sin(t)]

    correct?

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