Mathematics

$$\displaystyle \int \dfrac {1-x}{1+x}$$


SOLUTION
$$\int {\cfrac{{1 - x}}{{1 + x}}dx} $$
$$\int {\left( {\cfrac{1}{{1 + x}} - \cfrac{x}{{1 + x}}} \right)dx} $$
$$\int {\left( {\cfrac{1}{{1 + x}} - \left( {\cfrac{{1 + x - 1}}{{1 + x}}} \right)} \right)dx} $$
$$\int {\left( {\cfrac{1}{{1 + x}} - 1 + \cfrac{1}{{1 + x}}} \right)dx} $$
$$\int {\cfrac{2}{{1 + x}}dx - \int {1} dx} $$
$$=2 \log (x+1) -x+c$$
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Subjective Medium Published on 17th 09, 2020
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