{1}{{x²+2x+2}} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.4
Integrate the functions in Exercises 86 to 108.

Question : 95 of 271

Marks: +1, -0

\frac{1}{\sqrt{x^2+2x+2}}

Solution:

Let

I=\int\frac{1}{\sqrt{x^2+2x+2}}\,dx

=\frac{dx}{\sqrt{(x+1)^2+1}}

\therefore I=\log\left| (x+1)+\sqrt{(x+1)^2+1} \right|+C

=\log\left| (x+1)+\sqrt{x^2+2x+2} \right|+C

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