integral of (t^2+2)/(t^2)

解

\int \frac{t ^{2} + 2}{t ^{2}} d t

t - \frac{2}{t} + C

解答ステップ

\int \frac{t ^{2} + 2}{t ^{2}} d t

拡張

\frac{t ^{2} + 2}{t ^{2}} : 1 + \frac{2}{t ^{2}}

= \int 1 + \frac{2}{t ^{2}} d t

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 d t + \int \frac{2}{t ^{2}} d t

\int 1 d t = t

\int \frac{2}{t ^{2}} d t = - \frac{2}{t}

= t - \frac{2}{t}

定数を解答に追加する

= t - \frac{2}{t} + C