integral of 5x^2+(2/x)^4

解

\int 5 x^{2} + (\frac{2}{x})^{4} d x

\frac{5 x ^{3}}{3} - \frac{16}{3 x ^{3}} + C

解答ステップ

\int 5 x^{2} + (\frac{2}{x})^{4} d x

簡素化

5 x^{2} + (\frac{2}{x})^{4} : 5 x^{2} + \frac{16}{x ^{4}}

= \int 5 x^{2} + \frac{16}{x ^{4}} 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 5 x^{2} d x + \int \frac{16}{x ^{4}} d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int \frac{16}{x ^{4}} d x = - \frac{16}{3 x ^{3}}

= \frac{5 x ^{3}}{3} - \frac{16}{3 x ^{3}}

定数を解答に追加する

= \frac{5 x ^{3}}{3} - \frac{16}{3 x ^{3}} + C