Mathematics

$$\displaystyle \int \frac{d\left ( x^{2}+1 \right )}{\sqrt{x^{2}+2}}$$ is equal to


ANSWER

$$\displaystyle 2\sqrt{x^{2}+2}+k$$


SOLUTION
$$\displaystyle \int \frac{d\left ( x^{2}+1 \right )}{\sqrt{x^{2}+2}}$$

$$\displaystyle I=\int  \frac { 2x }{ \sqrt { x^{ 2 }+2 }  } dx$$

Put $$x^{ 2 }+2=t$$
$$\Rightarrow  2xdx=dt$$

$$\displaystyle I=\int  \frac { 1 }{ \sqrt { t }  } dt$$
$$\Rightarrow \displaystyle I=2\sqrt{t}+k$$
$$I=2\sqrt { x^{ 2 }+2 } +k$$
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