Question

Evaluate:$\int\sqrt{x^{2}+2x+5}dx$

• A. $-\frac{1}{2}\left(x+1\right)\sqrt{x^{2}+2x+5} +2log \left|\left(x+1\right)+\sqrt{x^{2}+2x+5} \right|+C $
• B. $\frac{1}{2}\left(x+1\right)\sqrt{x^{2}+2x+5} +2log \left|\left(x+1\right)+\sqrt{x^{2}+2x+5} \right|+C $
• C. $-\frac{1}{2}\left(x+1\right)\sqrt{x^{2}+2x+5} -2log \left|\left(x+1\right)+\sqrt{x^{2}+2x+5} \right|+C $
• D. None of these

Answer 1

Answer: (B)

$ I =\int\sqrt{x^{2} + 2x + 5 }dx =\int\sqrt{\left(x+1\right)^{2}+\left(2^{2}\right)}dx$

$\Rightarrow I= \frac{1}{2}\left(x+1\right)\sqrt{x^{2}+2x+5} +2log \left|\left(x+1\right)+\sqrt{x^{2}+2x+5} \right|+C $