{x²+4x+6} - NCERT Class XII Mathematics Chapter - - Solutions

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.7
Integrate the functions in Exercises 158 to 166.

Question : 160 of 271

Marks: +1, -0

\sqrt{x^2+4x+6}

Solution:

Let

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

=\sqrt{x^2+4x+4+2}dx

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

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

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

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