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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 7.9
Evaluate the definite integrals in Exercises 176 to 195.
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Question : 186 of 271
Marks: +1, -0
∫23dxx2−1\int\limits_{2}^{3}\frac{dx}{x^2-1}
Solution:  
∫23dxx2−1\int\limits_{2}^{3}\frac{dx}{x^2-1}
=[12log⁡(x−1x+1)]23=\left[\frac{1}{2}\log\left(\frac{x-1}{x+1}\right)\right]_{2}^{3}
=12[log⁡(3−13+1)−log⁡(2−12+1)]=\frac{1}{2}\left[\log\left(\frac{3-1}{3+1}\right)-\log\left(\frac{2-1}{2+1}\right)\right]
=12[log⁡(24)−log⁡(13)]=\frac{1}{2}\left[\log\left(\frac{2}{4}\right)-\log\left(\frac{1}{3}\right)\right]
=12log⁡32=\frac{1}{2}\log\frac{3}{2}
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