Integrate- - - 1 1 d x - x 2 - 2 x - 5

[ ∫ _ #160; ^ #160; 1 x^ 2 +2x+5 dx=∫ _ #160; ^ #160; 1 ( x+1 ) #160; ^ 2 +4 dx #160; ...

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Definite Integral as Limit of Sum

Integrate: ...

Question

Integrate:
$\int_{- 1}^{1} \frac{d x}{x^{2} + 2 x + 5}$

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Solution

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\int_{- 1}^{1} \frac{d x}{x^{2} + 2 x + 5}

1 \int - 1 \frac{d x}{(1 + e^{x}) (1 + x^{2})}

\int_{- 1}^{1} \frac{d x}{1 + x^{2}} =

\frac{x + 3}{x^{2} - 2 x - 5}

The value of the definite integral $\int_{- 1}^{1} \frac{d x}{(1 + e^{x}) (1 + x^{2})}$ is

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