Mathematics

$$\int _{ -1 }^{ 1 }{ \frac { dx }{ { x }^{ 2 }+2x+5 }  }$$


SOLUTION
$$\displaystyle \int _{-1}^{1}\dfrac {dx}{x^2+zx+5}$$
$$\displaystyle \int _{-1}^{1}\dfrac {1}{(x+1)^2+4}dx$$
$$\dfrac {1}{2}\tan^{-1}\dfrac {(x+1)}{2}|_{-1}^{1}$$
$$\dfrac {1}{2}\tan^{-1} \left (\dfrac {2}{2}\right)-\dfrac {1}{2}\tan^{-1}\left (\dfrac {-1+1}{2}\right)$$
$$\dfrac {1}{2}\tan^{-1} 1-\dfrac {1}{2}\tan^{-1}0$$
$$\dfrac {1}{2} \left (\dfrac {\pi}{4}\right)-\dfrac {1}{2}(0)\ \Rightarrow \dfrac {\pi}{8}-0=\boxed {\dfrac {\pi}{8}}$$

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Subjective Medium Published on 17th 09, 2020
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