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

解

\int_{2}^{4} (\frac{2}{x} + 3 x)^{2} d x

193

解答ステップ

\int_{2}^{4} (\frac{2}{x} + 3 x)^{2} d x

簡素化

(\frac{2}{x} + 3 x)^{2} : \frac{4}{x ^{2}} + 12 + 9 x^{2}

= \int_{2}^{4} \frac{4}{x ^{2}} + 12 + 9 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_{2}^{4} \frac{4}{x ^{2}} d x + \int_{2}^{4} 12 d x + \int_{2}^{4} 9 x^{2} d x

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

\int_{2}^{4} 12 d x = 24

\int_{2}^{4} 9 x^{2} d x = 168

= 1 + 24 + 168

簡素化

= 193