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Integrate the function
$\sqrt{x^2+4 x+1}$
$\sqrt{x^2+4 x+1}$
Solution:
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Verified Answer
$\int \sqrt{x^2+4 x+1} d x=\int \sqrt{(x+2)^2-(\sqrt{3})^2} d x$
$=\frac{x+2}{2} \sqrt{x^2+4 x+1}-\frac{3}{2} \log \left|(x+2)+\sqrt{\left(x^2+4 x+1\right)}\right|+C$
$=\frac{x+2}{2} \sqrt{x^2+4 x+1}-\frac{3}{2} \log \left|(x+2)+\sqrt{\left(x^2+4 x+1\right)}\right|+C$
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