{x²+4x+1} - NCERT Class XII Mathematics Chapter - - Solutions

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 161 of 271

Marks: +1, -0

\sqrt{x^2+4x+1}

Solution:

Let

I=\int\sqrt{x^2+4x+1}\,dx

=\int\sqrt{(x^2+4x+4)-3}\,dx

=\int\sqrt{(x+2)^2-(\sqrt{3})^2}\,dx

=\frac{x+2}{2}\sqrt{(x+2)^2-(\sqrt{3})^2}-\frac{3}{2}\log\left|(x+2)+\sqrt{(x+2)^2-(\sqrt{3})^2}\right|+C

=\frac{x+2}{2}\sqrt{x^2+4x+1}-\frac{3}{2}\log\left|(x+2)+\sqrt{x^2+4x+1}\right|+C

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