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Evaluate \( \int_{0}^{2} \frac{5 x+4}{x^2+4} \) |
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Answer» \(\int_0^2 \frac{5x+4}{x^2+4}dx\) = \(\frac{5}{2}\)\(\int_0^2 \frac{2x}{x^2+4}dx\) + 4 \(\int_0^2 \frac{1}{x^2+4}dx\) = \(\frac{5}{2}\)\([log(x^2+4)]_0^2\) + \(\frac{4}{2}[tan^{-1}\frac{x}{2}]_0^2\) = \(\frac{5}{2}\)(log 8 - log 4) + 2 (tan-11 - tan-10) = \(\frac{5}{2}\)log \(\frac{8}{4}\) + 2(\(\frac{\pi}{4}-0\)) = \(\frac{5}{2}\) log 2 + \(\frac{\pi}{2}\) |
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