x^2+2 x+5 d x=___ - Vidyadip

MCQ

$\int \sqrt{x^2+2 x+5} d x=$___

A
$(x+1) \sqrt{x^2+2 x+5}+\log \left[(x+1)+\sqrt{x^2+2 x+5}\right]+ c$
B
$(x+2) \sqrt{x^2+2 x+5}+\log \left[(x+2)+\sqrt{x^2+2 x+5}\right]+ c$
C
$\left(\frac{ x +2}{2}\right) \sqrt{x^2+2 x+5}+\frac{1}{2} \log \left[(x+2)+\sqrt{x^2+2 x+5}\right]+ c$
✓
$\left(\frac{ x +1}{2}\right) \sqrt{x^2+2 x+5}+2 \log \left[(x+1)+\sqrt{x^2+2 x+5}\right]+ c$

✓

Answer

Correct option: D.

$\left(\frac{ x +1}{2}\right) \sqrt{x^2+2 x+5}+2 \log \left[(x+1)+\sqrt{x^2+2 x+5}\right]+ c$

$\left(\frac{ x +1}{2}\right) \sqrt{x^2+2 x+5}+2 \log \left[(x+1)+\sqrt{x^2+2 x+5}\right]+ c$

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