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\( \int_{1}^{2} \frac{(x+1)^{3}}{x^{2}} d x \) |
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Answer» \(\int\limits^2_1 \frac{(x + 1)^3}{x^2}dx\) \(= \int\limits^2_1 \left(x + 3 + \frac3x + \frac1{x^2}\right)dx\) \(= \left(2 + 6 +3log2 - \frac12\right)- \left(\frac12 + 3+ 3log1-1\right)\) \(= 8 + 3log2 - \frac12 - \frac12 - 2\) \((\because log 1 = 0)\) \(= 5 + 3log2\) |
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