integral of (5x^2+2/(x^4)-3\sqrt[3]{x})

解

\int (5 x^{2} + \frac{2}{x ^{4}} - 3 3 x) d x

\frac{5 x ^{3}}{3} - \frac{2}{3 x ^{3}} - \frac{9}{4} x^{\frac{4}{3}} + C

解答ステップ

\int 5 x^{2} + \frac{2}{x ^{4}} - 3 3 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 5 x^{2} d x + \int \frac{2}{x ^{4}} d x - \int 3 3 x d x

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

\int \frac{2}{x ^{4}} d x = - \frac{2}{3 x ^{3}}

\int 3 3 x d x = \frac{9}{4} x^{\frac{4}{3}}

= \frac{5 x ^{3}}{3} - \frac{2}{3 x ^{3}} - \frac{9}{4} x^{\frac{4}{3}}

定数を解答に追加する

= \frac{5 x ^{3}}{3} - \frac{2}{3 x ^{3}} - \frac{9}{4} x^{\frac{4}{3}} + C