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Find: \( \int \frac{2x+1}{\sqrt{x^{2}+10x+9}} d x \) |
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Answer» \(\int\frac{2x+1}{\sqrt{x^2+10x+9}}\)dx = \(\int\frac{2x+10-9}{\sqrt{x^2+10x+9}}dx\) = \(\int\frac{2x+10}{\sqrt{x^2+10x+9}}dx\) - 9\(\int\frac{1}{\sqrt{(x+5)^2-16}}dx\) = 2\(\sqrt{x^2+10x+9}\) - 9log|x + 5 + \(\sqrt{x^2+10x+9}\)| + c |
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