_{-1}¹ {dx}{x²+2x+5} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.10
Evaluate the definite integrals in Exercises 198 to 205 using substitution.

Question : 204 of 271

Marks: +1, -0

\int\limits_{-1}^{1} \frac{dx}{x^{2}+2x+5}

Solution:

Let

I=\int\limits_{-1}^{1} \frac{dx}{x^{2}+2x+5}

=\int\limits_{-1}^{1} \frac{dx}{x^{2}+2x+1+4}

=\int\limits_{-1}^{1} \frac{dx}{(x+1)^{2}+2^{2}}

=\frac{1}{2}\left[\tan^{-1}\frac{x+1}{2}\right]_{-1}^{1}

=\frac{1}{2}\left[\tan^{-1}1-\tan^{-1}0\right]

=\frac{1}{2}\times\frac{\pi}{4}=\frac{\pi}{8}

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