Mathematics

Evaluate:
$$\displaystyle \int  \sqrt {x^2+4x+5 } dx$$ 


SOLUTION

Now,
$$\displaystyle \int  \sqrt {x^2+4x+5 } dx$$ 
$$=\displaystyle \int  \sqrt {x^2+4x+4+1 } dx$$ 
$$=\displaystyle \int  \sqrt {(x+2)^2+1^2 } dx$$ 
$$=\dfrac{(x+2)\sqrt{(x+2)^2+1^2}}{2}+\dfrac{1}{2}\log\left|(x+2)+\sqrt{(x+2)^2+1^2}\right|+c$$ [ Where $$c$$ is integrating constant]
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Subjective Medium Published on 17th 09, 2020
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