Mathematics

Solve:

$$\displaystyle \int_{1}^{2} \dfrac {x}{(x+1)(x+2)}dx$$


SOLUTION

$$I=\displaystyle \int_{1}^2\dfrac {x}{(x+1)(x+2)}dx$$ 

$$=\displaystyle \int_{1}^2 \left (-\dfrac {1}{x+1} +\dfrac {2}{x+2} \right)dx$$

$$\Rightarrow \ I=\left [-\log (x+1)+2 \log (x+2)\right]_1^2 $$ 

$$=\left [\log \dfrac {(x+2)^2}{x+1}\right]_1^2$$ 

$$=\log \dfrac {16}{3}-\log \dfrac {9}{2}$$ 

$$=\log \dfrac {32}{27}$$
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Subjective Medium Published on 17th 09, 2020
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