Mathematics

$$\displaystyle \int \dfrac{d}{dx}(\tan^{-1}{x})dx=$$_______$$+c$$


SOLUTION

We have,

$$\int{\dfrac{d}{dx}\left( {{\tan }^{-1}}x \right)dx}$$


On first differentiating and we get,

$$\int{\dfrac{1}{1+{{x}^{2}}}}dx$$


On integrating and we get,

$$\int{\dfrac{1}{1+{{x}^{2}}}}dx={{\tan }^{-1}}x+c$$


Hence, this is the answer.
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Subjective Medium Published on 17th 09, 2020
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