integral from 1 to infinity of 2/(x^2+2)

解答

\int_{1}^{\infty} \frac{2}{x ^{2} + 2} d x

\frac{π}{2} - 2 arctan (\frac{1}{2})

十进制

1.35102 \dots

求解步骤

\int_{1}^{\infty} \frac{2}{x ^{2} + 2} d x

计算不定积分:

\int \frac{2}{x ^{2} + 2} d x = 2 arctan (\frac{x}{2}) + C

带入上下限计算后得:

\int_{1}^{\infty} \frac{2}{x ^{2} + 2} d x = \frac{π}{2} - 2 arctan (\frac{1}{2})

= \frac{π}{2} - 2 arctan (\frac{1}{2})

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