Mathematics

Integrate $$\displaystyle \int \dfrac {x}{x+10}dx$$


ANSWER

$$x-10\ln|x+10|+C$$


SOLUTION
$$\displaystyle\int{\dfrac{x}{x+10}dx}$$

$$=\displaystyle\int{\dfrac{x+10-10}{x+10}dx}$$

$$=\displaystyle\int{\dfrac{x+10}{x+10}dx}-10\displaystyle\int{\dfrac{dx}{x+10}}$$

$$=\displaystyle\int{dx}-10\displaystyle\int{\dfrac{dx}{x+10}}$$

$$=x-10\ln{\left|x+10\right|}+C$$
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Single Correct Medium Published on 17th 09, 2020
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