Giải thích các bước giải:
$I_2=\int\sqrt{x^2+2x+5}dx$
$\to I_2=\int\sqrt{(x+1)^2+4}dx$
$\to I_2=2\int\sqrt{(\dfrac{x+1}{2})^2+1}dx$
$\to I_2=4\int\sqrt{(\dfrac{x+1}{2})^2+1}d(\dfrac{x+1}{2})$
$\to I_2=4\left(\dfrac{1}{8}\left(x+1\right)\sqrt{x^2+2x+5}+\dfrac{1}{2}\ln \left|\dfrac{x+1+\sqrt{x^2+2x+5}}{2}\right|\right)+C$