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人気のある微分積分 >

integral from 0 to 0.27 of ln(1+x^2)

解

\int_{0}^{0.27} ln (1 + x^{2}) d x

解

0.00642 \dots

解答ステップ

\int_{0}^{0.27} ln (1 + x^{2}) d x

部分積分を適用する

= [x ln (1 + x^{2}) - \int \frac{2 x ^{2}}{1 + x ^{2}} d x]_{0}^{0.27}

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

= [x ln (1 + x^{2}) - 2 (- arctan (x) + x)]_{0}^{0.27}

限度を計算する:

0.00642 \dots

= 0.00642 \dots

グラフ

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