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

解

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

\frac{28}{3}

十進法表記

9.33333 \dots

解答ステップ

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

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{1}^{3} x^{2} d x = \frac{26}{3}

\int_{1}^{3} \frac{1}{x ^{2}} d x = \frac{2}{3}

= \frac{26}{3} + \frac{2}{3}

簡素化

\frac{26}{3} + \frac{2}{3} : \frac{28}{3}

= \frac{28}{3}