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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 : 188 of 271
Marks: +1, -0
∫23xdxx2+1\int\limits_{2}^{3} \frac{xdx}{x^2+1}
Solution:  
∫23xdxx2+1\int\limits_{2}^{3} \frac{xdx}{x^2+1} =∫232xx2+1= \int\limits_{2}^{3} \frac{2x}{x^2+1}
=12[log⁡(x2+1)]23= \frac{1}{2} \left[ \log(x^2+1) \right]_{2}^{3}
=12[log⁡10−log⁡5]= \frac{1}{2} [\log 10 - \log 5]
=12log⁡105=12log⁡2= \frac{1}{2} \log \frac{10}{5} = \frac{1}{2} \log 2
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