Mathematics

$$\displaystyle \int \frac{2-x^{2}}{1+x^{2}}dx.$$


ANSWER

$$\displaystyle -x+3\tan ^{-1}x$$


SOLUTION
$$ \displaystyle \int  \frac { 2-x^{ 2 } }{ 1+x^{ 2 } } dx=\int  \frac { -x^{ 2 }-1+3 }{ x^{ 2 }+1 } dx$$

$$ \displaystyle =\int  \left( -1+\frac { 3 }{ x^{ 2 }+1 }  \right) dx=-x+3\tan ^{ -1 } x$$
Hence, option 'C' is correct.
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Single Correct Medium Published on 17th 09, 2020
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