integral from 1 to 3 of (8x^2-7x+5)/x

解

\int_{1}^{3} \frac{8 x ^{2} - 7 x + 5}{x} d x

5 ln (3) + 18

十進法表記

23.49306 \dots

解答ステップ

\int_{1}^{3} \frac{8 x ^{2} - 7 x + 5}{x} d x

拡張

\frac{8 x ^{2} - 7 x + 5}{x} : 8 x - 7 + \frac{5}{x}

= \int_{1}^{3} 8 x - 7 + \frac{5}{x} 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} 8 x d x - \int_{1}^{3} 7 d x + \int_{1}^{3} \frac{5}{x} d x

\int_{1}^{3} 8 x d x = 32

\int_{1}^{3} 7 d x = 14

\int_{1}^{3} \frac{5}{x} d x = 5 ln (3)

= 32 - 14 + 5 ln (3)

簡素化

= 5 ln (3) + 18