integral from 1 to 2 of (x^5+5x^8)/(x^4)

解

\int_{1}^{2} \frac{x ^{5} + 5 x ^{8}}{x ^{4}} d x

\frac{65}{2}

十進法表記

32.5

解答ステップ

\int_{1}^{2} \frac{x ^{5} + 5 x ^{8}}{x ^{4}} d x

拡張

\frac{x ^{5} + 5 x ^{8}}{x ^{4}} : \frac{x ^{5}}{x ^{4}} + \frac{5 x ^{8}}{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{5 x ^{8}}{x ^{4}} d x

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

\int_{1}^{2} \frac{5 x ^{8}}{x ^{4}} d x = 31

= \frac{3}{2} + 31

簡素化

\frac{3}{2} + 31 : \frac{65}{2}

= \frac{65}{2}