Mathematics

Solve $$\int^{3}_{2}\dfrac {x}{x^{2}-1}dx$$


ANSWER

$$\dfrac{1}{2}ln(\dfrac{8}{3})$$


SOLUTION
Let, $$x^2-1=t$$

$$\implies 2x.dx=dt$$

Substituting values , we get

$$\implies \int \dfrac{dt}{2t}$$

$$\implies \dfrac{1}{2}lnt$$

$$\implies \dfrac{1}{2}[ln(x^2-1)]^3_2$$

$$\implies \dfrac{1}{2}ln(\dfrac{8}{3})$$
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Single Correct Medium Published on 17th 09, 2020
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