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  • Integrate the functions in Exercises 1 to 9. root of x^2 + 4 x + 6

Integrate the functions in Exercises 1 to 9.

    Q3.    \sqrt{x^2 + 4x + 6}

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Given function \sqrt{x^2 + 4x + 6},

So, let us consider the function to be;

I = \int\sqrt{x^2 + 4x + 6}dx

 = \int\sqrt{(x^2 + 4x + 4)+2}dx = \int\sqrt{(x + 2)^2 +(\sqrt2)^2}dx

And we know that, \int \sqrt{x^2+a^2}dx = \frac{x}{2}\sqrt{x^2+a^2}+\frac{a^2}{2}\log|x+\sqrt{x^2+a^2}| +C

\Rightarrow I = \frac{x+2}{2}\sqrt{x^2+4x+6}+\frac{2}{2}\log\left | (x+2)+\sqrt{x^2+4x+6} \right |+C

= \frac{x+2}{2}\sqrt{x^2+4x+6}+\log\left | (x+2)+\sqrt{x^2+4x+6} \right |+C

 

Posted by

Divya Prakash Singh

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