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Title: Integration by Partial Fraction Decomposition
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Series: Real Analysis
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Chapter: Riemann Integral
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YouTube-Title: Real Analysis 59 | Integration by Partial Fraction Decomposition
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Bright video: https://youtu.be/dLYIijHqH9U
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Dark video: https://youtu.be/LdMx0VUEfik
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Exercise Download PDF sheets
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: ra59_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Which of the following functions is a rational function?
A1: $f(x) = \frac{\sin(x)}{x}$
A2: $f(x) = \frac{x^2}{x-\exp(x)}$
A3: $f(x) = \frac{x}{1+x^2}$
A4: $f(x) = \frac{-1}{\tan(x)}$
Q2: What is not an antiderivative of the function $f: \mathbb{R}\setminus {0} \rightarrow \mathbb{R}$ given by $f(x) = \frac{1}{x}$?
A1: $$F(x) = \log(|x|)$$
A2: $$F(x) = \log(|x|) + 2$$
A3: $$F(x) = \begin{cases} \log(|x|) + 2 ,,& x > 0 \ \log(|x|) - 1 ,,& x < 0 \end{cases}$$
A4: $$ F(x) = \log(x) $$
Q3: What is the integral $\int_4^5 \frac{1}{x(x+1)}, dx$?
A1: $\log(5) - \log(6) - \log(4) + \log(5)$
A2: $- \log \left( \frac{25}{24} \right)$
A3: $\log(5) - \log(4)$
A4: $0.04$
A5: $e$
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Last update: 2025-01
