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人気のある微分積分 >

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

解

\int_{1}^{3} \frac{2 x}{( x ^{2} + 3 ) ^{2}} d x

解

\frac{1}{6}

+1

十進法表記

0.16666 \dots

解答ステップ

\int_{1}^{3} \frac{2 x}{( x ^{2} + 3 ) ^{2}} d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{1}^{3} \frac{x}{( x ^{2} + 3 ) ^{2}} d x

u置換積分法を適用する

= 2 \cdot \int_{4}^{12} \frac{1}{2 u ^{2}} d u

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \frac{1}{2} \cdot \int_{4}^{12} \frac{1}{u ^{2}} d u

べき乗則を適用する

= 2 \cdot \frac{1}{2} [- \frac{1}{u}]_{4}^{12}

簡素化

2 \cdot \frac{1}{2} [- \frac{1}{u}]_{4}^{12} : [- \frac{1}{u}]_{4}^{12}

= [- \frac{1}{u}]_{4}^{12}

限度を計算する:

\frac{1}{6}

= \frac{1}{6}

グラフ

人気の例

integral from 3 to 11 of x^2

\int_{3}^{11} x^{2} d x

integral from 1 to 2 of xsqrt(x^2+1)

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

integral from 0 to pi of (1+cos(θ))^2

\int_{0}^{π} (1 + cos (θ))^{2} d θ

integral from-1 to 1 of sin(npix)

\int_{- 1}^{1} sin (nπ x) d x

integral from 1 to 9 of sqrt(6x-5)

\int_{1}^{9} 6 x - 5 d x