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integration of (x²+1)/(x+1)² dx |
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Answer» \(\int\frac{x^2+1}{(x+1)^2}dx\) = \(\int \frac{x^2+1+2x-2x}{(x+1)^2}dx\) = \(\int \frac{(x+1)^2}{(x+1)^2}dx\) - \(\int \frac{2x+2-2}{(x+1)^2}dx\) = \(\int dx\) - \(\int \frac{2(x+1)}{(x+1)^2}dx\) + \(2\int \frac{1}{(x+1)^2}dx\) = \(\int dx\) - \(2\int \frac{1}{(x+1)}dx + 2\) + \(2\int \frac{1}{(x+1)^2}dx\) = x - 2 log (x + 1) - \(\frac{2}{x+1}\) + C |
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