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人気のある微分積分 >

integral from 0 to infinity of 3/(x^2+1)

解

\int_{0}^{\infty} \frac{3}{x ^{2} + 1} d x

解

\frac{3 π}{2}

+1

十進法表記

4.71238 \dots

解答ステップ

\int_{0}^{\infty} \frac{3}{x ^{2} + 1} d x

不定積分を計算する:

\int \frac{3}{x ^{2} + 1} d x = 3 arctan (x) + C

限度を計算する:

\int_{0}^{\infty} \frac{3}{x ^{2} + 1} d x = 3 \cdot \frac{π}{2} - 0

= 3 \cdot \frac{π}{2} - 0

簡素化

= \frac{3 π}{2}

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