integral from 1 to 2 of (x^5+3x^6)/(x^4)

解

\int_{1}^{2} \frac{x ^{5} + 3 x ^{6}}{x ^{4}} d x

\frac{17}{2}

十進法表記

8.5

解答ステップ

\int_{1}^{2} \frac{x ^{5} + 3 x ^{6}}{x ^{4}} d x

拡張

\frac{x ^{5} + 3 x ^{6}}{x ^{4}} : \frac{x ^{5}}{x ^{4}} + \frac{3 x ^{6}}{x ^{4}}

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}^{2} \frac{x ^{5}}{x ^{4}} d x + \int_{1}^{2} \frac{3 x ^{6}}{x ^{4}} d x

\int_{1}^{2} \frac{x ^{5}}{x ^{4}} d x = \frac{3}{2}

\int_{1}^{2} \frac{3 x ^{6}}{x ^{4}} d x = 7

= \frac{3}{2} + 7

簡素化

\frac{3}{2} + 7 : \frac{17}{2}

= \frac{17}{2}