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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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$\int(2x^2-3 \, sin x+5 \sqrt{x})dx$