$\int \sqrt{x^{2} + 2x + 5} \, dx$ is equal to
$\frac{1}{2} \left( (x+1)\sqrt{x^{2} + 2x + 5} + 2\log|x+1+\sqrt{x^{2} + 2x + 5}|\right) + C$
$(x+1)\sqrt{x^{2} + 2x + 5} + 2\log|x+1+\sqrt{x^{2} + 2x + 5}| + C$
$(x+1)\sqrt{x^{2} + 2x + 5} - 2\log|x+1+\sqrt{x^{2} + 2x + 5}| + C$
$(x+1)\sqrt{x^{2} + 2x + 5} + \frac{1}{2}\log|x+1+\sqrt{x^{2} + 2x + 5}| + C$
